b) Two PINS are chosen independently and at random, and you are given that each consists of four different digits. Let X be the random variable denoting the number of digits that the two PINS have in common. i. Explain clearly why P(X = k) = ,for k (0, 1, 2, 3, 4. () ii. Hence write down the values of the probability mass function of X, and find its mean.
b) Two PINS are chosen independently and at random, and you are given that each consists of four different digits. Let X be the random variable denoting the number of digits that the two PINS have in common. i. Explain clearly why P(X = k) = ,for k (0, 1, 2, 3, 4. () ii. Hence write down the values of the probability mass function of X, and find its mean.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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Transcribed Image Text:b) Two PINS are chosen independently and at random, and you are given that each PIN consists
of four different digits. Let X be the random variable denoting the number of digits that the two
PINS have in common.
i. Explain clearly why P(X = k) =-
for k = 0, 1, 2, 3, 4.
ii. Hence write down the values of the probability mass function of X, and find its mean.
![Given that a random variable X have a Poisson distribution with A;
Find E[cos(nX)] if E(X) = In 2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03eca7d1-e303-4e98-9bb8-b1587cfb6271%2F41dd0f4a-8601-4859-97d7-0d61df77bb92%2F0vxvhce_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given that a random variable X have a Poisson distribution with A;
Find E[cos(nX)] if E(X) = In 2
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