The sample space of a random experiment is {a,b.c,d,e,f}, and each outcomes is equally likely. A random variables is define as follows, determine the probability mas function of X for c,e,f are:- outcome a
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- A. Free Throw Shot - A player is awarded free throws whenever the player is fouled in a shooting motion. A free throw is counted as one point if the ball went in the basket and zero if it misses. Based on Piel's stats in his previous games, he makes 60% of his free throws. To improve, he shots 5 free throws every day in practice. Suppose the random variable, X, is the number of times Piel makes a basket in 5 free throw attempts. This illustrates a random experiment following a distribution with number of trials, n, equal to and probability of making a basket, p, equal to Accordingly, below is the probability distribution table for the number of baskets made in his practice, X. X P[X = x] 0 1 2 0.0102 0.0768 0.2304 3 0.3456 In his practice, the probability that he can get 2 to 4 points is the chance that he will make a perfect score is 4 0.2592 5 WhileSuppose the probability of having blood type A is 0.10. Let X be the number of people with type A in the experiment of selecting one thousand random people. 1. The values of the random variable X is x = _____. A. {1, 2, …} B. {0, 1, 2, …} C. {1, 2, …, 1000} D. {0, 1, 2, …, 1000} 2. Which of the following is(are) correct? Then, explain whyI. The probability of each value of x is between 0 & 1II. The probability that one thousand people will have blood type B is 1 A. I onlyB. II onlyC. Both I and IID. Neither I nor IIA dice is thrown followed by throwing coins, the number of times the currency is tossed depends on the outcome of the dice that comes out. Suppose X denotes the random variable value of the number that appears on the toss of the dice and Y denotes the random variable resulting from the number of faces (M) that appears on the toss of a coin. a. Complete the probability with X and Y by filling in the table below: Y 0 1 2 3 4 LO 5 1/12 1/12 1 1/24 2/24 c. Find the marginal distribution of Y! d. Are X and Y independent? 2 X 3 4 6 a. Determine the formula for the joint probability mass function X and Y! b. Find the marginal distribution of X! 5
- Determine the value/s of the random variable in each of the following situations: A box contains three colors of marbles - white, black, and yellow. Three balls are picked one at a time with replacement. Let U be the number of yellow marbles that appear. A. 3 B. 1 C. 0 D. 0, 1, 2, 3 E. 0, 1, 2 F. 0, 1 G. 2The table below shows the results of a survey that asked 1079 adults from a certain country if they favored or opposed a tax to fund education. A person is selected at random. Complete parts (a) through (c). =TTTE Support Oppose Unsure Total Males 171 332 8 511 Females 245 298 25 568 Total 416 630 33 1079 (a) Find the probability that the person opposed the tax or is female. P(opposed the tax or is female) =| (Round to the nearest thousandth as needed.) (b) Find the probability that the person supports the tax or is male. P(supports the tax or is male) =| (Round to the nearest thousandth as needed.) (c) Find the probability that the person is not unsure or is female. P(is not unsure or is female) = (Round to the nearest thousandth as needed.)Let a function of random variable X is given by ( refer pictures) : a) Find the value of K b) Form the table of probability distribution of X C) Find the mean and variance of the distribution
- A test of 100 motor is done to determine the defective motors. The probability that a motor is defective is 0.02. The motors defects are independent random variable. The probability that exactly two motors are defective given that the number of defective motors is two or fewer is: Select one: a. 0.3127 b. 0.5846 c. 0.5364 d. 0.404 e. 0.4773Show your work for thisM3