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The number of home runs scored by a certain team in one baseball game is a random variable with the distribution (pmf), f(x) = P[X = x] What is the probability of scoring at least 1 home run in a game? Given that the team scores at least one home run in a game, what is the probability that it scores two? Find the mean number of home runs per game Find the standard deviation of home runs per game

Solution

a)

P(at least 1) = P(1) + P(2) = 0.2 + 0.1 = 0.3 [ANSWER]

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b)

P(2|at least 1) = P(2)/P(at least 1) = 0.1/0.3 = 0.33333333333 [ANSWER]

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c)

a)

P(at least 1) = P(1) + P(2) = 0.2 + 0.1 = 0.3 [ANSWER]

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b)

P(2|at least 1) = P(2)/P(at least 1) = 0.1/0.3 = 0.33333333333 [ANSWER]

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c)

Thus,      
      
E(x) = Expected value = mean =    0.4 [ANSWER]  

d)

Var(x) = E(x^2) - E(x)^2 =    0.44  

s(x) = sqrt [Var(x)] =    0.663324958   [ANSWER]
      

x	P(x)	x P(x)	x^2 P(x)
0	0.7	0	0
1	0.2	0.2	0.2
2	0.1	0.2	0.4