II.A random variable X has the following probability distribution Value of X 1 2 3 4 5 Find the following: A. Determine the value of c. B. Find P(x = 1) C. Find P(I 2) P(X=x) 2c 5c 6c 7c 20c
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- The joint probability distribution function of X and Y is given by: 1 2 3 1 0.05 0.06 0.10 X 2 0.13 0.21 0.30 a. Find the conditional distribution of Y given X = 1 b. Find the conditional distribution of X given Y = 2 5 0.02 0.03 0.10Suppose that the random variable xx, shown below, represents the number of speeding tickets a person received in a three-year period. P(x)P(x) represents the probability of a randomly selected person having received that number of speeding tickets during that period. Use the probability distribution table shown below to answer the following questions. xx P(x)P(x) 0 0.3377 1 0.3347 2 0.1744 3 0.0605 4 0.0464 5 0.0463 6+ 0.0000 a) What is the probability that a randomly selected person has received four tickets in a three-year period?P(x=4)=P(x=4)=b) What is the probability that a randomly selected person has received four or more tickets in a three-year period?P(x≥4)=P(x≥4)=c) What is the probability that a randomly selected person has received more than four tickets in a three-year period?P(x>4)=P(x>4)=d) Would it be unusual to randomly select a person who has received four tickets in a three-year period? Yes No e) Which probability should we use to…Let X = number of siblings. Use the following table to answer questions 3 and 4: x (p)x 0 2/40 1 5/40 2 0 3 14/40 4 7/40 5 4/40 3. Find the probability that a person has two siblings.a. 8/40b. 8c. 2d. 6/404. Find the expected number of siblings a person has.a. 2.78b. 15c. 3.13d. 1.0
- 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 9Q P.6: On its way, a car meets 4 traffic lights, and the probability that each of them will be red is 0.5. Let X be a discrete random variable equal to the number of traffic lights that were green when the car arrived. X may take the values of 0, 1, 2, 3, 4. (Assume traffic lights are independent.) What is the probability distribution of X? The probability distribution of X is 3 4 p(x) 0.5 0.25 0.125 0.0625 0.0625 The probability of distribution of X is 3 p(x) 0.5 0.5 0.25 0.125 The probability of distribution of X is 3 4 p(x) 0.5 0.25 0.5 0.25 0.125 The probability distribution of X is 1 3 4 p(x) | 0.5 || 0.5 || 0.5 | 0.5 || 0.5 The probability of distribution of X is 3 4 p(x) || 0.0625 0.0625 0.125 0.25 0.5Assume that 12 jurors are selected from a population in which 50% of the people are Mexican-Americans. The random variable x is the number of Mexican-Americans on the jury. x 0 1 2 3 4 5 6 7 8 9 10 11 12 P(x) 0.0000.000 0.0030 0.0160 0.0540 0.1210 0.1930 0.2260 0.1930 0.1210 0.0540 0.0160 0.0030 0.0000 A. Find the probability of exactly 2 Mexican-Americans among 12 jurors. P(2)equals= b. Find the probability of 2 or fewer Mexican-Americans among 12 jurors. c. Does 2 Mexican-Americans among 12 jurors suggest that the selection process discriminates against Mexican-Americans? Why or why not?
- Rem. A concerned parents group determined the number of commercials shown in each of the five children's programs over a period of time. Num of Commercials P(X = x 1.824 0.078 2.081 0.05 2.338 0.101 2.595 0.134 2.852 0.07 3.109 0.567 Consider the probability distribution table above. Determine the following: (a) Determine the mean = (b) Determine the Standard DeviationX 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 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 would you expect a physics major to spend doing post-graduate research?Suppose that the random variable x, shown below, represents the number times . P(x) represents the probability of a randomly selected person having received that number of speeding tickets during that period. Use the probability distribution table shown below to answer the following questions. 19 a| P(x) 0 0.2749 Rectangular Snip 1 0.2522 2 0.2511 3 0.1494 4 0.0455 0.0269 6+ 0.0000 a) What is the probability that a randomly selected person has received two tickets in a three-year period? P(x = 2) %3D b) What is the probability that a randomly selected person has received four tickets in a three-year period? P(x = 4) c) What is the probability that that a randomly selected person has received more than five tickets in a three-year period? P(x > 5) = d) What is the probability that that a randomly selected person has received three or less tickets in a three-year period? P(x < 3)
- 2. A random variable|x has the following probability distribution. Find the value of p and then evaluate the following probabilities: P(X 5) and P(0 < X < 6). Find the mean of the probability distribution. 1 3 4 6 17 P(X) 2p 2p 3p p2 2p2 7p? + p Value of p = P(X < 5) =. P(X 2 5) = P(0 < X < 5) = Mean (u) =action=edit&resid=C08701F6876D7727!330&ithint=file%2cdocx&action=edit&wdNewAndOpenCt=1654742848849&wd Previous Ses 1. The following table shows the probability distribution for X = the number of traffic accidents reported in a day in a small city in the Rockies. X P(X) 0 0.25 1 0.30 0.20 0.10 0.10 5 0.05 a. What is the mear or expected number of accidents? b. What is the standard deviation of the number of accidents? an alarm in the presence of 2 3 4
