If a random variable follows a Poisson distribution with l

\"If a random variable follows a Poisson distribution
with l   =   20 and t   = 1/2 find the
a. expected value, variance, and standard deviation of this Poisson distribution
b. probability of exactly 8 successes\"
Please explain how these are solved. Thanks.

Solution

Poisson distribution has a parameter = It

= 10

Hence parameter l = 10

a) Mean of Poisson = l = 10

Variance = l = 10

Std dev = rt 10 = 3.162

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Prob for 8 successes = 0.1126