Chapter 5.3, Problem 2E

Find the cdf of a random variable Y whose pdf is given by; 2, 0≤x≤1 1/3, 0≤x≤1 a) f(x)=3, 2≤x≤4 0, elsewhere 2, 1≤x≤2 b) f(x)= (3-x)2, 2≤x≤3 0, elsewhere

For all integers a and b, a + b is not ≡ 0(mod n) if and only if a is not ≡ 0(mod n)a or is not b ≡ 0(mod n). Is conjecture true or false?why?

or W Annuities L Question 2, 5.3.7 > Find the future value for the ordinary annuity with the given payment and interest rate. PMT = $2,000; 1.65% compounded quarterly for 11 years. The future value of the ordinary annuity is $ (Do not round until the final answer. Then round to the nearest cent as needed.) example Get more help Q Search 30 L

There are m users who share a computer system. Each user alternates between "thinking" intervals whose durations are independent exponentially distributed with parameter Y, and an "active" mode that starts by submitting a service re- quest. The server can only serve one request at a time, and will serve a request completely before serving other requests. The service times of different requests are independent exponentially distributed random variables with parameter μ, and also independent of the thinking times of the users. Construct a Markov chain model and derive the steady-state distribution of the number of pending requests, including the one presently served, if any.

Use laplace to transform.

In order to find probability, you can use this formula in Microsoft Excel: The best way to understand and solve these problems is by first drawing a bell curve and marking key points such as x, the mean, and the areas of interest. Once marked on the bell curve, figure out what calculations are needed to find the area of interest. =NORM.DIST(x, Mean, Standard Dev., TRUE). When the question mentions “greater than” you may have to subtract your answer from 1. When the question mentions “between (two values)”, you need to do separate calculation for both values and then subtract their results to get the answer. 1.  Compute the probability of a value between 44.0 and 55.0. (The question requires finding probability value between 44 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 44, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the…

If a uniform distribution is defined over the interval from 6 to 10, then answer the followings: What is the mean of this uniform distribution? Show that the probability of any value between 6 and 10 is equal to 1.0 Find the probability of a value more than 7. Find the probability of a value between 7 and 9.   The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $20 and $30 per share. What is the probability that the stock price will be: More than $27? Less than or equal to $24?   The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches. What is the mean amount of rainfall for the month? What is the probability of less than an inch of rain for the month? What is the probability of exactly 1.00 inch of rain? What is the probability of more than 1.50 inches of rain for the month? The best way to solve this problem is begin by creating a chart. Clearly mark the range, identifying the lower and upper…

Problem 1: The mean hourly pay of an American Airlines flight attendant is normally distributed with a mean of 40 per hour and a standard deviation of 3.00 per hour. What is the probability that the hourly pay of a randomly selected flight attendant is: Between the mean and $45 per hour? More than $45 per hour? Less than $32 per hour?   Problem 2: The mean of a normal probability distribution is 400 pounds. The standard deviation is 10 pounds. What is the area between 415 pounds and the mean of 400 pounds? What is the area between the mean and 395 pounds? What is the probability of randomly selecting a value less than 395 pounds?   Problem 3: In New York State, the mean salary for high school teachers in 2022 was 81,410 with a standard deviation of 9,500. Only Alaska’s mean salary was higher. Assume New York’s state salaries follow a normal distribution. What percent of New York State high school teachers earn between 70,000 and 75,000? What percent of New York State high school…

For all integers a and b if a is congruent to 0(mod n) and b is congruent to 0(mod n) then a+b is congruent 0(mod n) DRAW A KNOW-SHOW TABLE: