Question 1171634: consider a binomial random variable X with n=5 and p=0.40
a. Find the probability distribution of X
b. Find P(X<3)
C. Find P(2<=X<=4)
d. Find the mean and the variance of X
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! mean is 5*0.4 or 2
variance is 2*0.6 or 1.2
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probability x=0 is 0.6^5=0.07776
probability x=1 is 5*0.4*0.6^4=0.2592
for x=2 is 5C2*0.4^2*0.6^3=0.3456
for x=3 it is 5C3*0.4^3*0.6^2=0.2304
for x=4 it is 5*0.4^4*0.6=0.0768
for x=5 it is 0.4^5=0.01024
for x<3, add the probabilities of x=0,1,2
for 2 < x < 4, add the probabilities of x=2,3, 4
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