Please show as much work, the video really did not help :(
Derive the cumulative distribution function (CDF) for a
exponential distribution
X∼exp(λ)
Calculate
P(X≥3) when
λ=2
(Correct answer is ~0.0025)
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Please show as much work, the video really did not help :(
Derive the cumulative distribution...
Let random variables X and Y have the bi-variate exponential CDF (cumulative distribution function) : F(x,y)...
Let random variables X and Y have the bi-variate exponential CDF (cumulative distribution function) : F(x,y) = 1 - exp(-x) - exp(-y) + exp(-x-y-xy) Given x > 0, y>0 a) Determine the probability that 4 < X given that Y = 2 b) Determine the probability that 4 < X given that Y is less than or equal to 2
2). Consider a discrete random variable X whose cumulative distribution function (CDF) is given by 0...
2). Consider a discrete random variable X whose cumulative distribution function (CDF) is given by 0 if x < 0 0.2 if 0 < x < 1 Ex(x) = {0.5 if 1 < x < 2 0.9 if 2 < x <3 11 if x > 3 a)Give the probability mass function of X, explicitly. b) Compute P(2 < X < 3). c) Compute P(x > 2). d) Compute P(X21|XS 2).
Suppose that X is a random variable whose cumulative distribution function (cdf) is given by: F(x)...
Suppose that X is a random variable whose cumulative distribution function (cdf) is given by: F(x) = Cx -x^2, 0<x<1 for some constant C a. What is the value of C? b. Find P(1/3 < X < 2/3) c. Find the median of X. d. What is the expected value of X?
Please answer me clearly so I can read well BSP2014 Tutorial 2 1. Check whether the...
Please answer me clearly so I can read well
BSP2014 Tutorial 2 1. Check whether the given function can serve as the probability mass function(p.m.f.) of a random variable 2forx-1,2, 3,4, 5 ii) Ax)for-0,1,2, 3,4 2. A random variable X has the following probability distribution. 0.1 2k 0.3 i)Find k ii)Evaluate PX2 and P-2X2) iii) Find the CDF of X 3. If X has the cumulative distribution function, CDF Fix) = I/2 , 1 xc3 x25 Find a) PXS 3)...
Problem 6. Consider a random variable X whose cumulative distribution function (cdf) is given by 0...
Problem 6. Consider a random variable X whose cumulative distribution function (cdf) is given by 0 0.1 0.4 0.5 0.5 + q if -2 f 0 r< 2.2 if 2.2<a<3 If 3 < x < 4 We are also told that P(X > 3) = 0.1. (a) What is q? (b) Compute P(X2 -2> 2) (c) What is p(0)? What is p(1)? What is p(P(X S0)? (Here, p(.) denotes the probability mass function (pmf) for X) (d) Sketch a plot...
5. The Exponential(A) distribution has density f(x) = for x<0' where λ > 0 (a) Show/of(x)...
5. The Exponential(A) distribution has density f(x) = for x<0' where λ > 0 (a) Show/of(x) dr-1. (b) Find F(x). Of course there is a separate answer for x 2 0 and x <0 (c Let X have an exponential density with parameter λ > 0 Prove the 'Inemoryless" property: P(X > t + s|X > s) = P(X > t) for t > 0 and s > 0. For example, the probability that the conversation lasts at least t...
Simple Probability Question, Please explain with details, thank you so much. Suppose that the cumulative distribution...
Simple Probability Question,
Please explain with details, thank you so much.
Suppose that the cumulative distribution function of the discrete random variable X is given by x V < 0 1L F(x) = { 1 +71 051 x < 2 1 VI Find P{X = 1}, P{X = 2}, P{X = 3} o 1, 11,1 OZ, ÉS 0 ];j; oh, o 12 Find P (} < X < ;) оооо Consider the following two functions S c(2x – 2y) 0...
please show thorough work Problem 3 Recall that X ~ Exp(A) if the probability density function...
please show thorough work
Problem 3 Recall that X ~ Exp(A) if the probability density function of X is fX(x)-Ae-λ r for z 2 0, Let Xi, , Xn ~ Exp(A), where λ is an unknown parameter. Exponential random variables are often used to model the time between rare events, in which case λ is interpreted as the average number of events occurring per unit of time a) Let zı, . . . , en be n observations of an...
y <0 1- e so y20 be the cumulative probability distribution function (CDF) for the random...
y <0 1- e so y20 be the cumulative probability distribution function (CDF) for the random variable Y-> the size (square footage) of a house with respect to the number of toilets. Let X be the number of toilets in the houses with respect to the size (square footage). a) Give the probability distribution function (PDF) for the random variable X f(x)- f(x) houses with 2049 square feet? (use at least four digits after the decimal if rounding...) c) Plot...
PLEASE SHOW ALL WORK 10. The cumulative distribution function (c.d.f) of a random variable X is...
PLEASE SHOW ALL WORK
10. The cumulative distribution function (c.d.f) of a random variable X is given by 1- Faro, -1/2, 1 0 otherwise. What is the probability that X will take a value greater than 2? A. 0.269 B. 0.950 C. 0.500 D. 0.368
2). Consider a discrete random variable X whose cumulative distribution function (CDF) is given by 0 if x < 0 0.2 if 0 < x < 1 Ex(x) = {0.5 if 1 < x < 2 0.9 if 2 < x <3 11 if x > 3 a)Give the probability mass function of X, explicitly. b) Compute P(2 < X < 3). c) Compute P(x > 2). d) Compute P(X21|XS 2).
Please answer me clearly so I can read well
BSP2014 Tutorial 2 1. Check whether the given function can serve as the probability mass function(p.m.f.) of a random variable 2forx-1,2, 3,4, 5 ii) Ax)for-0,1,2, 3,4 2. A random variable X has the following probability distribution. 0.1 2k 0.3 i)Find k ii)Evaluate PX2 and P-2X2) iii) Find the CDF of X 3. If X has the cumulative distribution function, CDF Fix) = I/2 , 1 xc3 x25 Find a) PXS 3)...
Problem 6. Consider a random variable X whose cumulative distribution function (cdf) is given by 0 0.1 0.4 0.5 0.5 + q if -2 f 0 r< 2.2 if 2.2<a<3 If 3 < x < 4 We are also told that P(X > 3) = 0.1. (a) What is q? (b) Compute P(X2 -2> 2) (c) What is p(0)? What is p(1)? What is p(P(X S0)? (Here, p(.) denotes the probability mass function (pmf) for X) (d) Sketch a plot...
5. The Exponential(A) distribution has density f(x) = for x<0' where λ > 0 (a) Show/of(x) dr-1. (b) Find F(x). Of course there is a separate answer for x 2 0 and x <0 (c Let X have an exponential density with parameter λ > 0 Prove the 'Inemoryless" property: P(X > t + s|X > s) = P(X > t) for t > 0 and s > 0. For example, the probability that the conversation lasts at least t...
Simple Probability Question,
Please explain with details, thank you so much.
Suppose that the cumulative distribution function of the discrete random variable X is given by x V < 0 1L F(x) = { 1 +71 051 x < 2 1 VI Find P{X = 1}, P{X = 2}, P{X = 3} o 1, 11,1 OZ, ÉS 0 ];j; oh, o 12 Find P (} < X < ;) оооо Consider the following two functions S c(2x – 2y) 0...
please show thorough work
Problem 3 Recall that X ~ Exp(A) if the probability density function of X is fX(x)-Ae-λ r for z 2 0, Let Xi, , Xn ~ Exp(A), where λ is an unknown parameter. Exponential random variables are often used to model the time between rare events, in which case λ is interpreted as the average number of events occurring per unit of time a) Let zı, . . . , en be n observations of an...
y <0 1- e so y20 be the cumulative probability distribution function (CDF) for the random variable Y-> the size (square footage) of a house with respect to the number of toilets. Let X be the number of toilets in the houses with respect to the size (square footage). a) Give the probability distribution function (PDF) for the random variable X f(x)- f(x) houses with 2049 square feet? (use at least four digits after the decimal if rounding...) c) Plot...
PLEASE SHOW ALL WORK
10. The cumulative distribution function (c.d.f) of a random variable X is given by 1- Faro, -1/2, 1 0 otherwise. What is the probability that X will take a value greater than 2? A. 0.269 B. 0.950 C. 0.500 D. 0.368
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