Question

Let X be a b (1, 1/2)RV, and consider all possible random samples of size 3...

Let X be a b (1, 1/2)RV, and consider all possible random samples of size 3 on X. Compute X bar and S2 for each of the eight samples, and compute the PMFs of X bar and s2

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Let X be Bernaulli random Variable with probability p = 1/2 ( i.e. Binomial random variables with n=1 and p=1/2).

The probability mass function of X is

Let Xbar and S2 be sample mean and sample variance respectively.

We have to draw sample of size 3 ( n=3)

The possible samples are ( 0,0,0) , ( 0, 0, 1) , ( 0, 1, 0), ( 0, 1, 1), ( 1, 0 ,0 ) , (1,1,0) ,(1, 0, 1) , (1,1,1).

Sample No. 1 2 3 Xbar S2
1 0 0 0 0 0.0000
2 0 0 1 0.3333 0.3333
3 0 1 0 0.3333 0.3333
4 0 1 1 0.6667 0.3333
5 1 0 0 0.3333 0.3333
6 1 0 1 0.6667 0.3333
7 1 1 0 0.6667 0.3333
8 1 1 1 1 0.0000

From table Xbar take 4 values 0, 0.3333, 0.6667, 1

and S2 take 2 values 0 and 0.3333.

The probability mass function ( PMF) of Xbar is

Xbar 0 0.3333 0.6667 1 Total
P(Xbar) 1/8 3/8 3/8 1/8 1

The probability mass function S2 is

S2 0 0.3333 Total
P(S2) 2/8 6/8 1
0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
91. Let X be a RV with support set {0, 1, 2}, p(1) = 0.3, and...
91. Let X be a RV with support set {0, 1, 2}, p(1) = 0.3, and p(2) = 0.5. Calculate E[X]. Let X be a discrete RV. Define the expected value E[X] of X. Is E[X] constant or random? Why? 92. Suppose X is a RV with support {−1,0,1} where p(−1) = q and p(1) = p. What relationship must hold between p and q to ensure that E[X] = 0? 93. Let X be a discrete RV and a,...
Let X be a continuous random variable rv distributed via the pdf f(x) =4e^(-4x) on the...
Let X be a continuous random variable rv distributed via the pdf f(x) =4e^(-4x) on the interval [0, infinity]. a) compute the cdf of X b) compute E(X) c) compute E(-2X) d) compute E(X^2)
Let X be a continuous RV with pdf f(x) = 2 ln x / x where...
Let X be a continuous RV with pdf f(x) = 2 ln x / x where 1 ≤ x ≤ e. Compute the standard deviation of X.
a) Let Z be a standart normal RV(random variable) and If Y = Z^2 for all...
a) Let Z be a standart normal RV(random variable) and If Y = Z^2 for all Z, what is the PDF and mean of Y ? b) If Y = Z^2 for Z>0 and Y=0 for other regitions, Calculate PDF of Y and P(Y=0). c) Calculate P(Y<1) by using table for both a and b options above.
Provide P (X ≥ 2).  Let X be a random variable. The set of all the possible...
Provide P (X ≥ 2).  Let X be a random variable. The set of all the possible values that X takes is ={0,1,2,3} Suppose X is a binomial random variable with success probability p = 0.6. Provide P (X ≥ 2). Why n here is 3, not 4?
Assume that a population of size 5 specifies that all possible samples of size "3" are...
Assume that a population of size 5 specifies that all possible samples of size "3" are extracted without repetition. Values: 2,500.00 2,650.00 2,790.00 3,125.00 3,200.00 1) Calculate the mean and standard deviation of the population. 2) Calculate all possible samples, their means and standard deviations. 3) Calculate the standard error of the means using the standard deviations. 4) Show that the expected value of the sample mean is equal to the mean of the population. 5) Show that the expected...
Let X be a random variable with possible values {−2, 0, 2} and such that P(X...
Let X be a random variable with possible values {−2, 0, 2} and such that P(X = 0) = 0.2. Compute E(X^2 ).
Given X ~ U(2, 27). Suppose that you form random samples of size 8 from this...
Given X ~ U(2, 27). Suppose that you form random samples of size 8 from this distribution. Answer the following, rounding probabilities to 4 decimals and everything else to 2 decimals.. a. The average of X-bar is and the standard deviation of X-bar is For the following, use the average and standard deviation found in part a. b. Find P(12 < X-bar < 14.5). d. Find the 72nd percentile of X-bar.
Let X be a discrete random variable with the range RX = {1, 2, 3, 4}....
Let X be a discrete random variable with the range RX = {1, 2, 3, 4}. Let PX(1) = 0.25, PX(2) = 0.125, PX(3) = 0.125. a) Compute PX(4). b) Find the CDF of X. c) Compute the probability that X is greater than 1 but less than or equal to 3.
Suppose we let X be a random variable that takes value 1, 2, 3 with equal...
Suppose we let X be a random variable that takes value 1, 2, 3 with equal probability. Then How many samples of X are needed on average to see all values at least once? Also, what if X is a random variable that takes values 1, 2 or 1,2,3,4? Thank you!
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT