MA 2631 Conference 4

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 = e

X.

2. Let X be a Poisson distributed random variable with parameter λ = 2.

a) Calculate

P [X ≥ 2 | X ≥ 1] .

b) Calculate

E

1

X + 1

.

3. Let Y be a Poisson distributed random variable with parameter λ, where λ is a non-negative integer.

Calculate

E [ |Y − λ| ] .

1

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