The probability function for the number of insurance policies John will sell to a customer is given by (2) f(x) = 0.5 – for X = 0, 1, or 2. (a) Is this a valid probability function? Explain your answer. Yes, f(x) > 0 and Ef(x) # 1 O Yes, f(x) > 0 and Ef(x) = 1 O No, f(x) > 0 and Ef(x) # 1 O No, f(x) > 0 and Ef(x) = 1 (b) What is the probability that John will sell exactly 2 policies to a customer? (Round your answer to three decimal places.) (c) What is the probability that John will sell at least 2 policies to a customer? (Round your answer to three decimal places.) (d) What is the expected number of policies John will sell? (Round your answer to three decimal places.) (e) What is the variance of the number of policies John will sell? (Round your answer to three decimal places.)

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Solve the following problems properly. A shipment of 8 television sets contains 3 defective sets. A hotel makes a random purchase of 4 these sets. If X is the number of defective sets purchased by the hotel, find (a0 the probability distribution and (b) the cumulative distribution of X. Using F(x), find (c) P(X = 2) and (d) P(0 < X <3).

Solve c,d

In a school sports day, each student is required to join at least one event. The following table represents the probability distribution function of the number of events (X) a student takes part in the sports day. 1 3 4. P(X=x) 0.25 0.375 1.5k k 0.05 (a) What is the value of k? (b) Find E(X) and o (X). (c) Suppose the number of events students take part are independent. In a group of 6 students, what is the probability that exactly 4 students join at least 2 events?

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For a particular disease, the probability that a patient passes away within the xth year is given by the following table:   xx P(x)P(x) 0 0.016 1 0.031 2 0.256 3 0.298 4 0.35 5 0.028 6 0.021   This means that the probability that someone passes away within the first year is 0.016. The probability that they pass away after one year would be 0.031.  What is the mean number of years someone survives?  (round to two decimal places) What is the standard deviation for the number of years someone survives?  (round to two decimal places) The Range Rule of Thumb for survival would be:  years to  years. (Round each to two decimal places.) In your own words, interpret what the Range Rule of Thumb tells us about this disease. (If you don't remember what the Range Rule of Thumb is, review the heading "Unusual Values" in the Learning Activities.)

In a football match, the winning team is given 2 points, and 0 point for the losing team. If the result is draw, 1 point is given to each team Assume X is the total number of points eaned after two matches. 5. (a) Construct a probability distribution function of x. (b) Find E(X) and Var (X) (c) Find the probability thata team wins in both matches. (d) Evaluate E (2X - 1).

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