Answer to Question #342652 in Statistics and Probability for Downer

Question #342652

A discrete random variable X is believe to follow a binomial distribution b(x; 5, p). If P(X = 0) = 243/1024, then find P(X = 3).

1
Expert's answer
2022-05-23T23:48:47-0400
"P(X=0)=\\dbinom{5}{0}(p)^{0}(1-p)^{5-0}=(1-p)^{5}"

"=\\dfrac{243}{1024}"

"1-p=\\dfrac{3}{4}"

"p=\\dfrac{1}{4}"

"P(X=3)=\\dbinom{5}{3}(\\dfrac{1}{4})^{3}(\\dfrac{3}{4})^{5-3}=\\dfrac{45}{512}"


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