3. The life X, in hours, of a certain kind of radio tube has a probability density function given by

fX(y) = 0 for y <100 and 100/y2 for y≥100.

a) What is the probability that a tube will survive 250 hours of operation?

b) Find the expected value of the random variable.

2. Let X be a discrete random variable, with probability distribution P(X = x1) = 0.25 and P(X = x2) = 0.75. Determine x1 and x2 such that E(X) = 10 and Var (X) = 48.

fX(y) = 0 for y <100 and 100/y2 for y≥100.

a) What is the probability that a tube will survive 250 hours of operation?

b) Find the expected value of the random variable.

2. Let X be a discrete random variable, with probability distribution P(X = x1) = 0.25 and P(X = x2) = 0.75. Determine x1 and x2 such that E(X) = 10 and Var (X) = 48.

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