Good day, kindly help with the circled question. Thanks (Hint: Use Theorem 1.12.)7.36 If X, and X, are independent random variables having the geometric dis-tribution with the parameter 8, show that Y=X, + X₂ is a random variablehaving the negative binomial distribution with the parameters and k = 2.7.37 IX and Y are independent random variables having the standard normaldistribution, show that the random variable Z = X + Y is also normallydistributed. (Hint: Complete the square in the exponent:) What are themean and the variance of this normal distribution?

We are given two independent random variables X1 and X2 such that both of them follow geometric…

Answered: 7.36 If X, and X, are independent…

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7.36 If X, and X, are independent random variables having the geometric dis- tribution with the parameter 8, show that Y=X, + X, is a random variable having the negative binomial distribution with the parameters and k = 2.