1. A test consists of 10 true-false questions. Suppose a student answers the que

Question

1. A test consists of 10 true-false questions. Suppose a student answers the questions by number correctly answered questions. (Hint: It might be helpful if you use relevant R commands to obtain the values of PMF and CDF.) (a) Give the expected value and variance of X (b) Find the probability the student will answer correctly exactly 5 of the questions c)Find the probability the student will answer correctly at most 5 of the questions. Use the cdf to answer this quesition. d) Let Y 10-X. In words, what does Y represent? (e) Use the edf to find P(2s Y s5)

Explanation / Answer

a) X follow binomial distribution with n = 10 , p = 1/2

E(X) = np = 5

var(X) = npq = 5/2

b) P(X =k) = nCk p^k* (1-p)^(n-k)

P(X =5) = 0.24609375

dbinom(5,10, 0.5)
[1] 0.2460938

c) P(X <=5) = 0.623046875

pbinom(5,10, 0.5)
[1] 0.6230469

d) Y represent the number of incorrect answers

e) P(2 < = Y <= 5)

= P(y<=5) - P(Y<=1)

= 0.6123047

pbinom(5,10, 0.5) - pbinom(1,10,0.5)
[1] 0.6123047

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