The multinomial joint probability mass function becomes the binomial probability mass function when k=
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- Suppose we roll 3 fair dice and let X be the number of twos we roll.(a) Find the probability mass function of X.(b) Find the expected value of X.(c) Find the variance of X.(d) Find the probability-generating function of X.(e) Find the moment-generating function of XClaims for a health company insurance are exponentially distributed. An insurance company offers the subscriber two different types of insurance, class A has a coverage of 1.54. For a random loss, with a probability of 0.640. Class B has a coverage of d. with a probability of 0.512. The value of d is:19 Help me answer the question
- Show work for every step. Two types of customers (Preferred and Regular) call a service center. Preferred customers call with rate 3 per hour, and Regular customers call with rate 5 per hour. The interarrival times of the calls for each customer type are exponentially distributed. If the call center opens at 8:00 AM, what is the probability that the first call (regardless of customers type who calls) is received before 8:15 AM?For each value of z*, find the cumulative probability P(Z s z*). (Round your answers to four decimal places.) AUSE SALT (a) z* = 1.96 (b) z* =-2.33 (c) z* = 2.58 (d) z* = 1.65If X is exponentially distributed, prove that the probability that X exceed its expected value is less than 0.5
- In a probability density function such as a Normal or bell-shaped curve, the area under the curve is used to make predictions about likelihoods and probabilities. What is the area (use a proportion) under the curve from the lowest possible value to the highest possible value?Telephone calls arrive at an exchange according to the Poisson process at a rate A= 2/min. Calculate the probability that exactly two calls will be received during each of the first 5 minutes of the hour.Fill in the P(X=x)values to give a legitimate probability distribution for the discrete random variable X, whose possible values are −2,1, 3, 4, and 5.
- (a) Sketch the probability mass function of X . (b) Find the mean and standard deviation of the number of pots of olives sold daily. (c) If the profit obtained from selling a pot of olives is 50p, what is the expected profit made on a single day? During a working week of 6 days?Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(X) using the normal distribution and compare the result with the exact probability. n=51 p=.03 x=20Three couples and two single individuals have been invited to an investment seminar and have agreed to attend. Suppose the probability that any particular couple or individual arrives late is 0.33 (a couple will travel together in the same vehicle, so either both people will be on time or else both will arrive late). Assume that different couples and individuals are on time or late independently of one another. Let X = the number of people who arrive late for the seminar. (a) Determine the probability mass function of X. [Hint: label the three couples #1, #2, and #3 and the two individuals #4 and #5.] (Round your answers to four decimal places.) 0 1 2 3 4 5 6 7 8 P(X=x) 0 1 2 3 4 5 6 7 0.1350 0.1330 0.2322 0.1965 0.2633 ✓ ✔ (b) Obtain the cumulative distribution function of X. (Round your answers to four decimal places.) F(x) 0.1350 0.268 0.5002 0.6967 x