Find the mean and the variance of the discrete random variable X, whose probability distribution is following table. 1 2 3 4 P(X =x) 1-k 2-3k 3-4k 4-6k
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- Find the variance and standard deviation of the probability distribution of a random variable X which can take only the values 3,5, and 7, given that P(3) 30 P(5) =, and P(7) = 20 13 %3D 2.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.Please calculate the covariance and the correlation coefficient for the two random variables and briefly comment on the resulting correlation between the variables.
- Imagine that you are training to run a half-marathon and so every week you have 2 intense days, 3 light days, and 2 rest days. On your intense days you run 16 km, on your light days you run 5 km, and on your rest days you do not run. How would you model your miles run per day as a random variable? (Hint: probability distribution)Company F sells fabrics known as fat quarters, which are rectangles of fabric created by cutting a yard of fabric into four pieces. Occasionally the manufacturing process results in a fabric defect. Let the random variable X represent the number of defects on a fat quarter created by Company F. The following table shows the probability distribution of X. X 0 1 2 3 4 or more Probability 0.58 0.23 0.11 0.05 0.03 If a fat quarter has more than 2 defects, it cannot be sold and is discarded. Let the random variable Y represent the number of defects on a fat quarter that can be sold by Company F. (a) Construct the probability distribution of the random variable Y. (b) Determine the mean and standard deviation of Y. Show your work. Company G also sells fat quarters. The mean and standard deviation of the number of defects on a fat quarter that can be sold by Company G are 0.40 and 0.66, respectively. The fat quarters sell for $5.00 each, but are discounted by…A random variable Y is given with its probability distribution. Find the value of 100q. 1 3 3q q Y P(Y) 0 0.35 2 0.25 4 9
- 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 59X 1 2 3. A physics professor wants to know what percent of physics majors will spend the next several years doing post-graduate research. He has the following probability distribution. 3 4 5 6 P(x) 0.35 0.20 0.15 0.10 0.05 x*P(x a. Define the random variable x. b. Define P(x), or the probability of x. c. Find the probability that a physics major will do post-graduate research for four years. P(x = 4) =_ d. Find the probability that a physics major will do post-graduate research for at most three years. P(x ≤ 3) =_ e. On average, how many years would you expect a physics major to spend doing post-graduate research?
