has the following information: P[F] = 0.5, P[HF] = 0.2, P[ MW] = 0.1 What is the sample space of the experiment? Find the following probabilities P[ W], P[MF], and P[ H].
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- Consider the table below gives the probabilities of the distribution of random variable X. Value of X P(X=x) (denoted by x) f(x) 0 1 2 3 4 567 00 8 0.14 b C 0.10 0.13 0.13 d 0.02 0.01 In reference to the table, suppose that b = f(1) =0.2 and c = f(2)= 0.06. What is the probability P(X ≥ 4) equal to?Given n independent policyholders with individual loss random variables X1, X2, ., Xn, such that the expected value of any policyholder's loss is pph and the variance is o. If the insurer is providing these n policyholders with insurance, find the following (the detailed steps are required): 1. The expected value of the insurer's average loss per policy; 2. The variance of the average loss per policy.Let x be a random variable that represents the batting average of a professional baseball player. Let y be a random variable that represents the percentage of strikeouts of a professional baseball player. A random sample of n = 6 professional baseball players gave the following information. x 0.336 0.296 0.340 0.248 0.367 0.269 y 3.2 7.5 4.0 8.6 3.1 11.1 (b) Use a 10% level of significance to test the claim that ρ ≠ 0. (Use 2 decimal places.) t critical t ± (d) Find the predicted percentage of strikeouts for a player with an x = 0.288 batting average. (Use 2 decimal places.) %(e) Find a 95% confidence interval for y when x = 0.288. (Use 2 decimal places.) lower limit % upper limit % (f) Use a 10% level of significance to test the claim that β ≠ 0. (Use 2 decimal places.) t critical t ± (g) Find a 95% confidence interval for β and interpret its meaning. (Use 2 decimal places.) lower limit upper limit please show steps and work
- It has been determined that the distribution of faulty products in a factory conforms to Poisson. 2% of the products produced monthly are defective. Calculate the probability of finding 3 defective parts in 250 randomly drawn samples.7a. 0.140b. 0.095c. 0.091D. 0.253to. 0.145Two six-sided dice are rolled and the random variable x is the sum of the values produced by each die. a. List the possible outcomes for the variable x, determine the probability for each outcome, and calculate the expected value of x. b. Calculate the variance of x. c. Calculate the standard deviation of x. a. List the possible outcomes for the variable x. Choose the correct answer below. O A. 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 О В. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 ОС. 1,2, 3, 4, 5, 6 O D. 3, 4, 5, 6, 7, 8, 9, 10, 11 Determine the probability for each outcome. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or fractions.) O A. P(1) =. P(2) = P(3) = P(4) = P(5) = P(6) = О В. Р/2)- P(3) = , P(4) = , P(5) = P(6) = P(7) = P(8) = P(9) = , P(10)= P(11) = P(12) = %3D O C. P(3) = P(4) = , P(5) = , P(6) = ,P(7) = P(8) = P(9) = P(10) = P(11) = O D. P(1)= , P(2) = , P(3) = P(4) = , P(5) = P(6) = P(7) = P(8) = P(9) = P(10) = P(11) = P(12)…Given Probabilities y = 1 y = 2 x = 1 x = 2 0.2 0.3 0.5 Find: а. Pr(X > Y) %3 b. Pr(Y = 1) =
- Let X be the random variable with the following distribution: x: -2 3 5 P(X=x): 0.3 0.2 0.5 Find the mean four decimal placesHow many combinations of k=5 screws is it possible to construct from n=8 different screws? What is the number of combinations of screws?B. A discrete random variable X has the following probability distribution: 1. 3 4. 1 2 P(X) y 6. 9. 9. 1. Find y. 2. Construct a probability histogram to describe P(X).
- Let Y = 3X – 1, where X is a random variable that is distributed uniformly from 10 to 50. Answer the following questions.a. What is the probability that X takes any value from 20 to 30? Draw the distribution and identify this probability in the distribution. Show your calculations.b. Calculate the expected value of X in addition to the variance and standard deviation of X. Show your calculations.c. Calculate the expected value of Y in addition to the variance and standard deviation of Y. Show your calculations.Q.6. Use the binomial distribution in which n 6 and p = 0.3 to %3D calculate the following probabilities: (a). X is at most 1. (b). X is at least 2. (c). X is more than 5. (d). X is less than 6.A random sample of n1 = 10 regions in New England gave the following violent crime rates (per million population). x1: New England Crime Rate 3.3 3.7 4.2 3.9 3.3 4.1 1.8 4.8 2.9 3.1 Another random sample of n2 = 12 regions in the Rocky Mountain states gave the following violent crime rates (per million population). x2: Rocky Mountain Crime Rate 3.9 4.1 4.5 5.5 3.3 4.8 3.5 2.4 3.1 3.5 5.2 2.8 Assume that the crime rate distribution is approximately normal in both regions. Do the data indicate that the violent crime rate in the Rocky Mountain region is higher than in New England? Use ? = 0.01. Solve the problem using both the traditional method and the P-value method. (Test the difference ?1 − ?2. Round the test statistic and critical value to three decimal places.) test statistic critical value