A random variable X has Poisson distribution with mean 2. Then P(X > 1.5) equals

2/e²

0

$1 minus 3 over straight e squared$

3/e²

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Solution

1 minus 3 over straight e squared

straight P space left parenthesis straight x space equals straight k right parenthesis space equals space straight e to the power of negative straight lambda end exponent space fraction numerator straight lambda to the power of straight k over denominator straight k factorial end fraction straight P left parenthesis straight x space greater or equal than space 2 right parenthesis space space equals 1 space minus space straight P space left parenthesis straight x space equals 0 right parenthesis space minus space straight P space left parenthesis straight x space equals 1 right parenthesis space equals space 1 minus straight e to the power of negative straight lambda end exponent space minus straight e to the power of negative straight lambda end exponent space open parentheses fraction numerator straight lambda over denominator 1 factorial end fraction close parentheses space equals space 1 minus 3 over straight e squared

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