1) Assume the random variable X has a binomial distribution with the given proba

Question

1) Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.

P(x<2), n=4, p= 0.8

2) Find the variance of the following data. Round your answer to one decimal place

3) Determine whether or not the distribution is a discrete probability distribution and select the reason why or why not.

First, decide whether the distribution is a discrete probability distribution, then select the reason for making this decision

Yes or No

Explanation / Answer

(1)

P(x<2) = P(x=0) + P(x=1)

P(x=0) = 4C0*0.80*0.24 = 0.0016

P(x=1) = 4C1*0.81*0.23 = 0.0256

So,

P(x<2) = 0.0016+0.0256 = 0.0272

(2)

E(X) = 6*0.2 + 7*0.2 + 8*0.1 + 9*0.2 + 10*0.3 = 8.2

E(X2) = 62*0.2 + 72*0.2 + 82*0.1 + 92*0.2 + 102*0.3 = 69.6

Variance of X = E(X2)-E(X)2 = 69.6-8.22 = 2.36

(3)

Yes, because sum of probabilities = 0.14+0.19+0.67 = 1

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