question 4 4) Consider the following experiment: We roll two dice. Let the events E, is the sum of the top facesis s.a) Compute each set E,b) Let us make the random variable X(E,) = s. List the chart of the random variable X. That is the tablewith X values on the left and probabilities on the right.c) Find Pr(X > 7)d) Consider a random variable Y as follows: Y= 1 IF Pr(X>7) AND Y= 0 otherwise.*** note this is a simple Bernoulli trial b(Y, Pr( X >7))Let us make the Bernoulli trial of 20 successive repetitions of the simple Bernoulli trial Y.That is b(Y,Pr(X>7), 20)Determine the following informationa) Pr(b(Y=18,Pr(X>7), 20))b) Notice that the Bernoulli trial b(Y=k,Pr(X>7), 20) gives us the probability that if we roll two dice twentytimes EXACTLY k times the sum of the faces on the two die is greater than 7.Find the following:The expected number of times that the faces will add up to a number greater than 7 in 20 trials of theBernoulli variable.The variance of this distribution.** Hint: We wish to calculate the following: E(b(Y,Pr(X>7), 20)) AND V(b(Y,Pr(X>7), 20))

Name: question 4 4) Consider the following experiment: We roll two dice. Let
Uploaded: 2024-03-20T07:07:50.000Z
Channel: Bartleby
Description: question 4 4) Consider the following experiment: We roll two dice. Let the events E, is the sum of the top facesis s.a) Compute each set E,b) Let us make the random variable X(E,) = s. List the chart of the random variable X. That is the tablewith X