X 1 2 3. A physics professor wants to know what percent of physics majors will spend the next several years doing post-graduate research. He has the following probability distribution. 3 4 5 6 P(x) 0.35 0.20 0.15 0.10 0.05 x*P(x D a. Define the random variable x. b. Define P(x), or the probability of x. c. Find the probability that a physics major will do post-graduate research for four years. P(x = 4) =_ d. Find the probability that a physics major will do post-graduate research for at most three years. P(x ≤ 3) =_ e. On average, how many years post-graduate research? would you expect a physics major to spend doing

A random variable Y is given with its probability distribution. Find the value of 100q. 1 3 3q q Y P(Y) 0 0.35 2 0.25 4 9

Do you carpool? Let  X  represent the number of occupants in a randomly chosen car on a certain stretch of highway during morning commute hours. A survey of cars showed that the probability distribution of  X  is as follows. x 1 2 3 4 5 Px 0.68 0.14 0.08 0.02 0.08 Send data to Excel   Part 1 of 7     (a) Find  P1 . P1  =  .68       Part 2 of 7     (b) Find  P (greater than or equal to  2 ). P (greater than or equal to  2 ) =  .32       Part 3 of 7     (c) Find the probability that a car has only one occupant. The probability that a car has only one occupant is    .       Part 4 of 7     (d) Find the probability that a car has fewer than four occupants. The probability that a car has fewer than four occupants is    .       Part 5 of 7     (e) Compute the mean  μx .…

A psychologist determined that the number of sessions required to obtain the trust of a new patient is either 1, 2, or 3. Let x be a random variable indicating the number of sessions re- quired to gain the patient's trust. The following probability function has been proposed. f(x) = for x = 1, 2, or 3 6. Is this probability function valid? Explain. b. What is the probability that it takes exactly two sessions to gain the patient's trust? с. What is the probability that it takes at least two sessions to gain the patient's trust?

A deck of four (4) cards has exactly one (1) color printed on each face – blue, yellow, red, or green. You have two (2) identical decks of this type. In this game, you randomly select a card from each of the two decks. Your score is the number of blue cards drawn – refer to this quantity as X. The probability distribution is below: X P(X) 0 0.5625 1 0.375 2 0.0625 1. If we replaced the yellow card in the first deck with another blue card, what would be the probability of drawing two blue cards? 2. If we replaced the yellow card in the first deck with another blue card, what distribution would the variable X follow?