2 Let x equal a real number that is selected randomly from the closed interval from zero to ten. Use your intuition to assign values to
for this follows uniform distribution
a) P{x: 0≤x≤3}= (3-0)/10=0.3
b) P{x: 0≤x≤10}= (10-0)/10 =1
c) P{x: x≥7}= (10-7)/10=0.3
2 Let x equal a real number that is selected randomly from the closed interval from...
Problem 2 Let x equal a real number that is selected randomly from the closed interval from zero to ten. Use your intuition to assign values to P{x: 0≤x≤3}=____________ P{x: x=3}=________________ P{x: 0≤x≤10}=_____________ P{x: x≥7}=_______________ P{x: 5<x≤9}=______________ E(X)=______________ Var(X)=______________ The standard deviation of X is ________ The mgf of X is M(t)=______________________ The cdf is F(x)=_______________________
A spinner from a board game randomly indicates a real number
between 0 and 20. The spinner is fair in the sense that it
indicates a number in a given interval with the same probability as
it indicates a number in any other interval of the same length.
(a) Explain why the functionf(x) =
f(x)=
0.05
if
0 ≤ x ≤ 20
0
if
x < 0 or x > 20
is a probability density function for the spinner's values?...
(5) 2. Let X be the number of packages being mailed by a randomly selected customer at a certain shipping facility. Suppose that the distribution of X is as follows: T 1 2 3 p(x) 3 .2 .5 A a random sample of size n-3 is selected. a) find pmf of Xn and construct a histogram, b) give two smallest values of S2, (S2 is the sample variance) and find their probabilities.
(5) 2. Let X be the number of...
Let X be the number of packages being mailed by a randomly selected customer at a certain shipping facility. Suppose the distribution of X is as follows. 1 0.3 2 0.4 3 0.1 4 0.2 p(x) (a) Consider a random sample of size n = 2 (two customers), and let X be the sample mean number of packages shipped. Obtain the probability distribution of X. 1 1.5 2 2.5 3 3.5 4 POCO (b) Refer to part (a) and calculate...
Let X be the number of packages being mailed by a randomly selected customer at a certain shipping facility. Suppose the distribution of X is as follows. x 1 P(x) 0.2 2 0.4 3 4 0.3 0.1 (a) Consider a random sample of size n = 2 (two customers), and let X be the sample mean number of packages shipped. Obtain the probability distribution of X. 1.5 35 (b) Refer to part (a) and calculate PX $ 2.5). (c) Again...
Let X be the number of packages being mailed by a randomly selected customer at a certain shipping facility. Suppose the distribution of X is as follows. * 1 p(x) 0.2 2 0.4 3 4 0.3 0.1 (a) Consider a random sample of size n 2 (two customers), and let X be the sample mean number of packages shipped. Obtain the probability distribution of X 1 1. 5 2 3.5 PC) 04 125 x 16 X (b) Refer to part...
Let x be the number of courses for which a randomly selected student at a certain university is registered. The probability distribution of x appears in the table shown below: x 1 2 3 4 5 6 7 p(x) .03 .05 .09 .26 .39 .14 .04 (a) What is P(x = 4)? P(x = 4) = (b) What is P(x ≤ 4)? P(x ≤ 4) = (c) What is the probability that the selected student is taking at most five...
12. Let f be integrable on a closed interval [a, b]. Suppose that there is a real number C such that f(x) 2C for all E a, b (1) Prove that if C>0, then 7 is also integrable on la,b] (6 Marks) (2) If C 0, i, still integrable (assuming f(x)关0 for any x E [aM)? If yes, supply a short proof. If no, give a counterexample. (6 Marks)
12. Let f be integrable on a closed interval [a, b]....
Consider the interval [0, 1]. Assume you randomly pick a real number in that interval with a probability density that is constant on that interval and write the number in decimal code. Give an argument for the following statement by using suitable Theorems and ideas from class: With probability equal to one the relative number of the figures “9” you see amongst the first n digits approaches 1/10 as n tends to infinity.
Let the random variable X count the number of adults out of five randomly selected adults who reported sleepwalking. The table gives the probability distribution of X X P(X=x) 0 0.142 1 0.353 2 3 0.137 4 0.042 5 0.006 A) Determine the missing probability that ensures the tables is a valid discrete probability distribution B) Compute the probability that among five randomly selected adults fewer than three report sleepwalking C) Compute the probability that among five randomly selected adults...