***Please show work or give an explanation** 1.) Consider the random experiment

Question

***Please show work or give an explanation**

1.) Consider the random experiment of tossing a fair coin four successive times. If a random variable X counts the number of tails in the coin toss, then X is a binomial random variable with parameters n = _____ and p = _____.

a. 4 ; 0.25
b. 4 ; 0.125
c. 4 ; 0.5
d. 4 ; 0.15
e. 4 ; 0.10

2.) X is a binomial random variable with parameters n = 10 and p = 0.7. Compute P(5).
a. 0.10
b. 0.17
c. 0.90
d. 0.83
e. 0.53

3.) Let us consider a dice to be rolled eight times. What is the probability that the face with two spots comes up exactly twice?
a. 0.17
b. 0.03
c. 0.24
d. 0.26
e. 0.53

Explanation / Answer

1) n = 4

p = P(tail) = 1/2 = 0.5

Option-C)

2) n = 10

p = 0.7

P(5) = 10C5 * 0.75 * (1 - 0.7)10-5

   = 0.10

Option-A) 0.10

3) n = 8

p = P(2 on a die) = 1/6 = 0.17

P(2 comes up exactly twice) = 8C2 * 0.172 * (1 - 0.17)8-2

                                          = 0.26

Option-D) 0.26

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