Question

In: Statistics and Probability

P(H)=2/3,P(T)=1/3, a coin is thrown 3times,X is a random variable that shows the number of getting head...

P(H)=2/3,P(T)=1/3, a coin is thrown 3times,X is a random variable that shows the number of getting head

a) find the distribution of X

b)find the expected value of X

c) find the variannce of X

d)find the standard deviation of X

Expert Solution

Solution:

Given:

P(H)=2/3

P(T)=1/3

n= number of times a coin is tossed =3

X = number of times getting head

Part a)

The distribution of X:

Since number of trials are fixed and are independent with probability of success = probability of getting head is fixed or constant for each trial, the distribution of X = number of times getting head follows Binomial distribution with parameters n=3 and p=2/3.

Part b)

Expected value of X is:

Part c)

The variance of X is

Part d)

The standard deviation of X

orchestra answered 1 year ago

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