Description
1. Consider the random variable X with the probability mass distribution
P[X = −1] = 0.3, P[X = 2] = 0.5, P[X = 5] = 0.1, P[X = 10] = 0.1.
Calculate the expected value and variance of X as well as the expectation of Y with Y = eX.
2. Let X be a Poisson distributed random variable with parameter λ = 2.
a) Calculate
P[X ≥ 2|X ≥ 1].
b) Calculate
.
3. Let Y be a Poisson distributed random variable with parameter λ, where λ is a non-negative integer. Calculate
E [ |Y − λ| ].
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