an unfair coin with P(H)=.25 is flipped 100 times. A random variable X= number of heads that occur Find the expected value and standard deviation

Question

please show as many steps as possible thank you

Answer 1

This is a binomial distribution B(n,p) with parameters n = 100 and p = 0.25 

 

E(X) = mean of X = n*p = 100 * .25 = 25

 

standard deviation = sqrt [ n*p*(1-p) ] = sqrt[ 100*.25*.75 ] = sqrt (18.75) ~ 4.33