Question

If the random variable X follows a binomial distribution with the probability of success given

by p, show that the variance of X is equal to np(1-p).

[Hint:Consider first a Bernoulli probability distribution with n=1.]

Answer #1

Assume the random variable X has a binomial distribution with
the given probability of obtaining success. Find the following
probability, given the number of trials and the probability of
obtaining success. Round your answer to four decimal places.
P(X≥7), n=10, p=0.3

A
random variable follows a binomial distribution with a probability
of success equal to 0.52. For a sample size of n=7, find the values
below.
a. the probability of exactly 3 successes
b. the probability of 4 or more successes
c. the probability of exactly 7 successes
d. the expected value of the random variable

A random variable follows a binomial distribution with a
probability of success equal to 0.69 For a sample size of N=11,
find the values below.
a. the probability of exactly 3 successes
b. the probability of 7 or more successes
c. the probability of exactly 10 successes
d. the expected value of the random variable

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>3) P ( X > 3 ) , n=7 n = 7 , p=0.5 p = 0.5

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≥10) P ( X ≥ 10 ) , n=14 , p=0.8

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>3)P(X>3), n=5, p=0.8

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≤4), n=6, p=0.8

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≥16), n=19, p=0.7

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≥7), n=10, p=0.5

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>4), n=7, p=0.4

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