Choose an American driver at random and let the random variable X be the number of speeding tickets the driver has received in the last two years. The discrete probability distribution of X is shown.

(2) Verify the two main requirements that make this a legitimate discrete probability distribution.

(6) Create a probability histogram for the random variable X.

(4) Explain in words what the probability P(Xââ?°¤2) means. What is the probability P(Xââ?°¤2)?

(3) Write the mathematical expression of the event that a randomly chosen driver has more than three speeding tickets in terms of the random variable X. What is the probability of this event?

(5) Compute and interpret E(X), the expected value of the random variable X.

Solution Preview

See attached file.

The conditions of a discrete probability distribution are:

1) the outcomes are finite (which is true in our case, since we have only 6 outcomes)
2) the sum of probabilities equal to 1 (which is also true since 0.16 + 0.32 + 0.25 + 0.12 + 0.09 + 0.06 ...

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