[Solved] MA2631 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 = 2.
   1. Calculate

P[X 2|X 1].

1. Calculate

.

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

E [ |Y | ].