There are 4 people at a party. Consider the random variable X=’number of people having the same birthday ’ (match only month, N=12). a. Define the sample space S and the associated probability function (pf). Plot pf. b. Plot the associated exceedance probability function G(x)=Pr[X>x]; c. Compute mean and standard deviation of X.

S = {0,2,3,4}

P(X=0) = 0.573 , P(X=2) = 0.401 , P(x=3) = 0.025, P(X=4) = 0.001

Mean = 0.879

Standard Deviation = 1.033

Step-by-step explanation:

Let the number of people having same birth month be = x

The number of ways of distributing the birthdays of the 4 men = (12*12*12*12)

The number of ways of distributing their birthdays = 12⁴

The sample space, S = { 0,2,3,4} (since 1 person cannot share birthday with himself)

P(X = 0) =

P(X=0) = 0.573

P(X=2) = P(2 months are common) P(1 month is common, 1 month is not common)

P(X=2) =

P(X=2) = 0.401

P(X=3) =

P(x=3) = 0.025

P(X=4) =

P(X=4) = 0.001

Mean,

Standard deviation,

SD = 1.033

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step-by-step explanation:

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step-by-step explanation: