A player takes 10 shots on a target and has probability 0.2 of hitting the target in each shot, independent of all other shots. Let X be the number of hits. Calculate and plot the PMF of X. What is the probability of scoring no hits? What is the probability of scoring more hits than misses? Find the expectation and the variance of X.

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Asked Nov 9, 2019
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A player takes 10 shots on a target and has probability 0.2 of hitting the target in each shot, independent of all other shots. Let X be the number of hits.
Calculate and plot the PMF of X.
What is the probability of scoring no hits?
What is the probability of scoring more hits than misses?
Find the expectation and the variance of X.

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Expert Answer

Step 1

From the given information, number of shots (n) = 10

                                                      Probability of hit, P (hit) = 0.2

Step 2

Let ‘X’ be a binomial distribution random variable

Formula for binomial probability

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P(X-x)nC,P (1-P)*

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Step 3

PMF (probability mass f...

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PMF of 'x nC,P (1-P)x-0,1,2,3,... n-x P(X-x)= ; otherwise 0

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