Show that the given formula is a probability mass function x = 1,2 7. P(x = x ) otherwise
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- A salesman has scheduled two appointments to sell encyclopedias. His first appointment will lead to a sale with probability 0.3, and his second will lead independently to a sale with probability 0.6. Any sale made is equally likely to be either for the deluxe model, which costs $1000, or the standard model, which costs $500. Determine the probability mass function of X, the total dollar value of all sales.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* = 1.65
- Suppose that the distribution function of X is given by: (0, b<0 b Osb<1 1 b F(b) =- D=1, Isb<2 2 11 2sb<3 12 b23 1. Determine its corresponding probability mass function. 3 2. FindFind the probability and draw the probability mass function of the following. The probability that a car will arrive at its destination is uniformly distributed from 30 minutes to 50 minutes. Find the probability that a person is arriving between 40 to 45 minutes.Fifty people were asked how much they paid for the last smartphone app they purchased. These data were collected. Let the random variable X be the price paid for the app, and let f(x)=P(X=x) be the probability mass function based on the result of this survey. Answer parts a through e below. a) Write f as a set of ordered pairs. (Type an ordered pair, using integers or decimals. Use a comma to separate answers as needed. Do not include the $ symbol in your answer.) Draw the probability distribution as a histogram. Choose the correct histogram below. OA OB. OC. Q Q Q Q Q Q b) Find the cumulative probability function F Price, x $1.00 $2.00 $3.00 $4.00 $5.00 $6.00 $7.00 OD. F(x)= (Type integers or decimals) c) Find f(4). f(4) = (Type an integer or a decimal.) What does f(4) represent? O A. The probability that a randomly selected person did not pay $4 for an app OB. The probability that a randomly selected person paid $4 for an app OC. The probability that a randomly selected person paid…
- Answer the last threea. Verify that f(x) is a valid probability mass function. b. Find the probability that the shuttle will be able to accommodate all ticketed people that show up. c. Say you are the 1st person on the wait list to get on the shuttle (that is to say if less than 4 people with tickets show up, you get a seat). What is the probability that you will be able to board the shuttle?The multinomial joint probability mass function becomes the binomial probability mass function when k = O 1 O 2 00
