x |
0 |
1 |
2 |
3 |
4 |
p(x) |
0.2 |
0.1 |
0.3 |
? |
0.1 |
i. The probability that a family owns three cars equals _______
ii. The probability that a family owns between 1 and 3 cars, inclusive, equals _______
iii. The expected number of cars equals _______
i) Since
ii) The probability that a family owns between 1 and 3 cars, inclusive, equals
iii) The expected number of cars equals
Let the random variable x represent the number of cars owned by a family. Assume that...
8. Let the random variable x represent the number of girls in a family with three children. Assume the probability of a child being a girl is 0.35 The table on the right describes the probability of having x number of girls. Determine whether the table describes a probability distribution. If it does, find the mean and standard deviation. Is it unusual for a family of three children to consist of three girls? x P(x) 0 0.275 1 0.444 2 ...
Let the random variable x represent the number of girls in a family with three children. Assume the probability of a child being a girl is 0.31. The table on the right describes the probability of having x number of girls. Determine whether the table describes a probability distribution. If it does, find the mean and standard deviation. Is it unusual for a family of three children to consist of three girls? 0 1 2 3 P(x) 0.329 0.443 0.199...
Let X represent the number of tires with low air pressure on a randomly chosen car.a. Which of the three functions below is a possible probability mass function of X? Explain.x0 1 2 3 4p1(x) 0.2 0.2 0.3 0.1 0.1p2(x) 0.1 0.3 0.3 0.2 0.2p3(x) 0.1 0.2 0.4 0.2 0.1b. For the possible probability mass function, compute ?x and ?x2.
2.1 Let X be a discrete random variable with the following probability distribution Xi 0 2 4 6 7 P(X = xi) 0.15 0.2 0.1 0.25 0.3 a) find P(X = 2 given that X < 5) b) if Y = (2 - X)2 , i. Construct the probability distribution of Y. ii. Find the expected value of Y iii. Find the variance of Y
4. In a population of 20 families, the number of cars owned by each family is given below: 0,2,2,3,1,1,4,2, 4,5,1,3,6,1,2,4, 3, 2,3, 3 Let X be the number of cars owned, and Xt be the possible values of X. Use this data to answer the following questions (a) Write down the relative-frequency distribution for X. (b) Find the median of number of cars owned. (c) Find the mean of number of cars owned. (d) Using (b) and (c), are there...
by cach family is given below Let X be the munber of cars owned, and X, be the pos- sible valus of X. Use this data to answer the following questions: (a) Write down the relative-frequency distribution for X (b) Find the median of number of cars owned. (c) Find the mean of mumber of cars owned (d) Using (b) and (c), are there more than 50% of values X, above the meau, or less? Explain your answe
Let X be a discrete random variable whose value is given by the number of successes observed on a series of 10 Bernoulli trials in which the probability of success is 1/3. Which of the following statements is or are true? I. X = B(10, 1/3) II. The only possible values of X are the integers 1 through 10 inclusive. III. If Y=10 - X, then Y = B(10, 2/3). A. I only B. I and II only C. I...
1. Let the random variable X represent the number of defective parts for a machine when 3 parts are sampled from a production line and tested. The following is the probability distribution of X 0 1 T0.38 2 3 х 0.10 0.01 0.51 (a) Compute expected value of the random variable X c) ) S 0. the l (b) Compute standard deviation of the random variable X (c) If g(X) = 2X +3, what is the expected value of g(X)?...
Let X be a random variable satisfying P(-1 X 1) = 0.3, P(X = 1.5) = 0.1, P(1.5 X P(3 X 7.4) 0.3, P(X 10)0.2 2) = 0.2 Find (i) P(X 2 1.3) (ii) P(X 2.3) ii P(1.5< X 2) (iv) P(1.5 3X 38)
Applied and Computational Questions 1. Pairs of random numbers (r, y) a. How many different pairs are possible? are generated. X and Y are integers between 0 and 5 inclusive. a random variable W is defined to equal the absolute value of the difference between X b. Suppose and Y. How many distinct values are possible for W? Give the pair of dice is rolled once. 2. Let x represent the number of times a one appears when a probability...