The mean value of the Gaussian probability distribution is numerically equal to its variance. True or False
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- An automotive center keeps track of customer complaints received each week. The probability distributions of complaints are shown below. The random variable, xi, represents the number of complaints, and p(xi) is the probability of receiving xi complaints for two of the stores. The cost impact of each complaint is believed to be y=$10x3 where x is the number of complaints. Store A xi 0 1 2 3 4 5 6 p(xi) 0.10 0.15 0.20 0.25 0.15 0.10 0.05 Store B xi 0 1 2 3 4 5 6 p(xi) 0.10 0.15 0.25 0.22 0.13 0.08 0.07 Sample from these distributions to compute the total number of complaints (store A+B) per week for 52 weeks.Neighborhood Insurance sells fire insurance policies to local homeowners. The premium is $150, the probability of a fire is 0.1%, and in the event of a fire, the insured damages (the payout on the policy) will be $140,000. g. What are the expected value and variance of your profit?The histogram shows the distribution of hurricanes that have hit a country from 1851 through 2015, where 1 is the weakest level and 5 is the strongest level. (a) Find the mean, variance, and standard deviation of the probability distribution. (b) Interpret the results. Hurricanes 123450.00.10.20.30.40.5CategoryProbability0.4070.2870.2260.0680.012 A histogram titled Hurricanes has a horizontal axis labeled Category from 1 to 5 in increments of 1 and a vertical axis labeled Probability from 0 to 0.5 in increments of 0.05. The histogram contains vertical bars of width 1, where one vertical bar is centered over each of the horizontal axis tick marks. The heights of the vertical bars are as follows, where the category is listed first and the height is listed second: 1, 0.407; 2, 0.287; 3, 0.226; 4, 0.068; 5, 0.012. Each bar is labeled with its height. (a) The mean is nothing. (Type an integer or a decimal. Do not…
- Find the characteristic function and probability generating function of geometric distribution.The annual premium for a $20,000 insurance policy against the theft of a painting is $350. If the (empirical) probability that the painting will be stolen during the year is 0.02, what is your expected return from the insurance company if you take out this insurance? Let X be the random variable for the amount of money received from the insurance company in the given year. E(X)= dollarsA small ferry runs every half hour from one side of a large river to the other. The probability distribution for the random variable Y = money collected (in dollars) on a randomly selected ferry trip is shown here. Money collected Probability P(Y ≤ 0) = 0 Incorrect 0.02 5 0.05 10 0.08 Calculate the cumulative probabilities. Do not round. 15 0.16 20 0.27 25 0.42 P(Y <5)= Incorrect
- Calculate xpectation and variance of X, if the probability distribution of the random variable X is given by X 1 0.3 f - 0 0.1 1 0.1 2 3 0.3 0.2 shodmFive males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the five who inherit the X-linked genetic disorder. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied. P(x) 0.032 1 0.161 2 0.307 3 0.307 4 0.161 5 0.032 Does the table show a probability distribution? Select all that apply. A. Yes, the table shows a probability distribution. B. No, the random variable x is categorical instead of numerical. C. No, the random variable x's number values are not associated with probabilities. D. No, not every probability is between 0 and 1 inclusive. E. No, the sum of all the probabilities is not equal to 1.An automotive center keeps track of customer complaints received each week. The probability distributions of complaints are shown below. The random variable, xi, represents the number of complaints, and p(xi) is the probability of receiving xi complaints for two of the stores. The cost impact of each complaint is believed to be y=$10x3 where x is the number of complaints. Store A xi 0 1 2 3 4 5 6 p(xi) 0.10 0.15 0.20 0.25 0.15 0.10 0.05 Store B xi 0 1 2 3 4 5 6 p(xi) 0.10 0.15 0.25 0.22 0.13 0.08 0.07 Compute the simulated averages and standard deviations of the number of complaints per week for each store and the total for both stores over the 52 weeks. Compare to the theoretical mean and standard deviations.
- Find the expected value for the random variable whose probability function graph is displayed here AP 0.5- 0.4- 0.3- 0.2- 0.1- 0- 1 2 34 5The normal distribution curve can be used as a probability distribution curve for normally distributed variables. Group of answer choices False TrueWe throw a fair dice. Let X denote the square of the difference between the smallest even number on the dice and the number appears on the dice. Determine the range and the probability distribution of X, draw the graph of the cumulative distribution function F of the random variable X and find the expected value and the variance of X.