Exercise 8. Alice and Bob are supposed to meet at 2pm. The number of hours Alice...
Exercise 8.
Alice and Bob are supposed to meet at 2pm. The number of hours
Alice is late is distributed uniformly over (0, 2). The number of
hours Bob is late is distributed according to an exponential random
variable with parameter 1. Their respective delays are supposed to
be independent. Let X be the time at which Alice and Bob actually
meet (in number of hours after 2pm).
(a) (4 points) Find the cumulative distribution function of
X.
(b) (2 points) Use it to calculate the probability density function
of X.
Homework Answers
Add Answer to:
Exercise 8.
Alice and Bob are supposed to meet at 2pm. The number of hours
Alice...
Exercise 7 (Ancilliarity) Choose one: 1. Let {X;} –1 be independent and identically distributed observations from...
Exercise 7 (Ancilliarity) Choose one: 1. Let {X;} –1 be independent and identically distributed observations from a location paramter family with cumulative distribution function F(x – 0), -00 < 0 < 0. Show that range of the distribution of R = maxi(Xi) – mini(Xi) does not depend on the parameter 8.) Hint: Use the facts that X1 = Z1 + 0 , ..., Xin = Zn + 0 and mini(Xi) = mini(Zi + 0), maxi(Xi) = maxi(Z; +0), where {Zi}=1...
2ND TEST IN PROBABILITY THEORY AND STATISTICS Variant 8 1. X is a continuous random variable with the cumulative distri...
2ND TEST IN PROBABILITY THEORY AND STATISTICS Variant 8 1. X is a continuous random variable with the cumulative distribution function if x<0 F(x)ax2 0.1x if osxs 20 if x> 20 0 Find 1) the coefficient a; 2) P 10); 3) P(X<30). 2. The result of some measurement X is normally distributed with parameters 184 and 8. Compute the probability that variable X takes value from interval (170;180) at least once in 5 experiments 3. Two independent random variables X...
3. (a) The bus 500 arrives at Liverpool Airport at a rate of A buses per...
3. (a) The bus 500 arrives at Liverpool Airport at a rate of A buses per hour. Assume that the arrivals form a Poisson process. Let X (t) be the number of buses that arrive in t hours. X(t) is distributed as Px(o(u)=e-Ar (Xt)" u! when u is a positive integer and 0 otherwise. Let Y be the amount of time that you must wait for the 3rd bus to arrive. The event X (t) < 3 (fewer than three...
Part 2. Random Variables 4. Two independent random variables Xand y are given with their distribution laws 0.3 0.7 0.8...
Part 2. Random Variables 4. Two independent random variables Xand y are given with their distribution laws 0.3 0.7 0.8 0.2 Pi Find the distribution law and variance for the random variable V-3XY 5. There are 7 white balls and 3 red balls in a box. Balls are taken from the box without return at randomm until one white ball is taken. Construct the distribution law for the number of taken balls. 6. Let X be a continuous random variable...
Instructions: If you require uniformly distributed random numbers in [0, 1], use Matlab’s built i...
Instructions: If you require uniformly distributed random
numbers
in [0, 1], use Matlab’s built in uniform random number generator
rand. Also,
you may NOT use any Matlab built-in functions that explicitly
perform the task
asked for in the problem.
Problem 6. Let α > 0 and set f(x)- ae-ale, for x e(-oo, oo). (a) Make a plot of f (b) Show that f is a probability density function (Hint: -, when z S 0, and x-r, when 0.) (c) If...
Let X be the total number of individuals of an endangered lizard species that are observed...
Let X be the total number of individuals of an endangered lizard species that are observed in a region on a given day. This observed number is assumed to be distributed according to a Poisson distribution with a mean of 3 lizards. The endangered lizards can belong to either of two sub-species: graham or opalinus. Let Y be the number of graham lizards observed during this study (note that the total observed number of any lizard is denoted by X,...
Structural steel is often treated with a protective coating (called an intumescent coating) that insulates the steel against damage from fire
1. The sampling distribution of the sample mean Structural steel is often treated with a protective coating (called an intumescent coating) that insulates the steel against damage from fire. Coatings are rated according to the number of hours of high-temperature exposure the treated steel can withstand, but if the coating is not applied with a mean thickness within the range specified by its manufacturer, the protection it provides will last for a shorter time than its rating. An office tower under construction...
For Exercises 3-15 to 3-18, verify that the following functions are probability mass functions, and determine...
For Exercises 3-15 to 3-18, verify that the following functions are probability mass functions, and determine the requested probabilities. 3-15. x 2 x)1/8 2/8 2/8 2/8 18 (a) P(Xs 1) (c) P(-1 X (b) P(X-2) (d) P(X--1 1) or X= 2) 3-28. The data from 250 endothermic reactions involving sodium bicarbonate are summarized as follow Final Temperature Conditions 266 K 271 K 274 K Number of Reactions 70 80 100 33. Determine the cumulative distribution function for the random variable...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
1. According to the paper, what does lactate dehydrogenase (LDH) do and what does it allow...
1. According to the paper, what does lactate dehydrogenase
(LDH) do and what does it allow to happen within the myofiber? (5
points)
2. According to the paper, what is the major disadvantage of
relying on glycolysis during high-intensity exercise? (5
points)
3. Using Figure 1 in the paper, briefly describe the different
sources of ATP production at 50% versus 90% AND explain whether you
believe this depiction of ATP production applies to a Type IIX
myofiber in a human....
Exercise 7 (Ancilliarity) Choose one: 1. Let {X;} –1 be independent and identically distributed observations from a location paramter family with cumulative distribution function F(x – 0), -00 < 0 < 0. Show that range of the distribution of R = maxi(Xi) – mini(Xi) does not depend on the parameter 8.) Hint: Use the facts that X1 = Z1 + 0 , ..., Xin = Zn + 0 and mini(Xi) = mini(Zi + 0), maxi(Xi) = maxi(Z; +0), where {Zi}=1...
2ND TEST IN PROBABILITY THEORY AND STATISTICS Variant 8 1. X is a continuous random variable with the cumulative distribution function if x<0 F(x)ax2 0.1x if osxs 20 if x> 20 0 Find 1) the coefficient a; 2) P 10); 3) P(X<30). 2. The result of some measurement X is normally distributed with parameters 184 and 8. Compute the probability that variable X takes value from interval (170;180) at least once in 5 experiments 3. Two independent random variables X...
3. (a) The bus 500 arrives at Liverpool Airport at a rate of A buses per hour. Assume that the arrivals form a Poisson process. Let X (t) be the number of buses that arrive in t hours. X(t) is distributed as Px(o(u)=e-Ar (Xt)" u! when u is a positive integer and 0 otherwise. Let Y be the amount of time that you must wait for the 3rd bus to arrive. The event X (t) < 3 (fewer than three...
Part 2. Random Variables 4. Two independent random variables Xand y are given with their distribution laws 0.3 0.7 0.8 0.2 Pi Find the distribution law and variance for the random variable V-3XY 5. There are 7 white balls and 3 red balls in a box. Balls are taken from the box without return at randomm until one white ball is taken. Construct the distribution law for the number of taken balls. 6. Let X be a continuous random variable...
Instructions: If you require uniformly distributed random
numbers
in [0, 1], use Matlab’s built in uniform random number generator
rand. Also,
you may NOT use any Matlab built-in functions that explicitly
perform the task
asked for in the problem.
Problem 6. Let α > 0 and set f(x)- ae-ale, for x e(-oo, oo). (a) Make a plot of f (b) Show that f is a probability density function (Hint: -, when z S 0, and x-r, when 0.) (c) If...
For Exercises 3-15 to 3-18, verify that the following functions are probability mass functions, and determine the requested probabilities. 3-15. x 2 x)1/8 2/8 2/8 2/8 18 (a) P(Xs 1) (c) P(-1 X (b) P(X-2) (d) P(X--1 1) or X= 2) 3-28. The data from 250 endothermic reactions involving sodium bicarbonate are summarized as follow Final Temperature Conditions 266 K 271 K 274 K Number of Reactions 70 80 100 33. Determine the cumulative distribution function for the random variable...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
1. According to the paper, what does lactate dehydrogenase
(LDH) do and what does it allow to happen within the myofiber? (5
points)
2. According to the paper, what is the major disadvantage of
relying on glycolysis during high-intensity exercise? (5
points)
3. Using Figure 1 in the paper, briefly describe the different
sources of ATP production at 50% versus 90% AND explain whether you
believe this depiction of ATP production applies to a Type IIX
myofiber in a human....
Most questions answered within 3 hours.
-
Potassium permanganate(KMNO4)is has a solubility of 6.4 g/ 100 g
of water at 20ºC, and 250...
asked 1 minute ago -
Given the following information:
acetic acid
CH3COOH
Ka = 1.8×10-5
triethylamine
(C2H5)3N
Kb = 5.2×10-4
(1)...
asked 4 minutes ago -
51.
As the marginal propensity to expend rises, the multiplier:
decreases.
is impossible to determine.
increases....
asked 8 minutes ago -
The Baldwin Company currently has the following balances on their
balance sheet:
Total
Liabilities
$69,309
Common...
asked 11 minutes ago -
A quiet town in Kansas has 10 people, all of whom have the same
preferences. There...
asked 16 minutes ago -
Summarize what an organization needs from a leader.
a. Analyze what might happen to an organization...
asked 19 minutes ago -
How would one critically evaluate an organizations marketing
strategies from the viewpoint of its consumers, as...
asked 18 minutes ago -
Given a standardized normal distribution (with μ = 0 and a σ =
1), what is...
asked 18 minutes ago -
Company XYZ know that replacement times for the quartz time
pieces it produces are normally distributed...
asked 33 minutes ago -
A) Write the acid-base reaction that occurs between Na2HPO4 and
NaOH
B) Write the possible reactions...
asked 47 minutes ago -
What advantages does the Natural Law Theory have in comparison
with the Divine Command Theory? Explain...
asked 53 minutes ago -
A diver comes off a board with arms straight up and legs
straight down, giving her...
asked 52 minutes ago