Question: 1.Let X be a geometric random variable with the probability of success being p = 0.25. If E[Y ] = 10, then what is the

1.Let X be a geometric random variable with the probability of success being p = 0.25. If E[Y ] = 10, then what is the expected value of 3X 2Y ?

2.A dashboard warning light is supposed to flash red if a car's oil pressure is too low. On a certain model, the probability of the light flashing when it should is 0.99. 2% of the time though it flashes for no apparent reason. If there is a 10% chance that the oil pressure really is low, what is the probability that the oil pressure is low if the warning light goes on?

3. Explain why we can say P(X < 5) = P(X 5) if X has normal distribution. Why may this not be the case if X has binomial distribution?

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