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)=(50)(p)0(1p)50=(1p)5P(X=0)=\dbinom{5}{0}(p)^{0}(1-p)^{5-0}=(1-p)^{5}

=2431024=\dfrac{243}{1024}

1p=341-p=\dfrac{3}{4}

p=14p=\dfrac{1}{4}

P(X=3)=(53)(14)3(34)53=45512P(X=3)=\dbinom{5}{3}(\dfrac{1}{4})^{3}(\dfrac{3}{4})^{5-3}=\dfrac{45}{512}


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