Question 1. X and Y are discrete random variables with the following joint distribution:Value of Y1422 30 40 6510.02 0.05 0.10 0.03 0.0150.17 0.15 0.05 0.02 0.018 0.02 0.03 0.15 0.10 0.09Value of XThat is, P(X= 1, Y = 14) = 0.02, and so forth.(1) Calculate the probability distribution, mean, and variance of Y.(2) Calculate the probability distribution, mean, and variance of Y given X = 8.(3) Calculate the covariance and correlation between X and Y.

Answered: Question 1. X and Y are discrete random…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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5.1.1 WP X 1.0 1.5 1.5 2.5 3.0 y 1 23+ 4 5 fxy(x, y) 1/4 1/8 1/4 1/4 1/8 5.2.2 WP Consider the joint distribution in Exercise 5.1.1. Determine the following: a. Conditional probability distribution of Y given that X = 1.5 b. Conditional probability distribution of X that Y = 2 c. E(Y | X = 1.5) d. Are X and Y independent?
QUESTION 8 Assume that Z is a standard normal random variable, find the following probabilities: 3.1. P(1.80 sZ s2.50) 3.2. P(Zs3.60) 3.3. P(Zs2) 3.4. P(Z21) 3.5. P(Zs-1.80).
For questions 1 - 4, answer the questions about discrete random variables. 1. Find the mean of the discrete random variable with the probability distribution below. 14- I X 1 2 3 4 5 P(x) 0.3 0.2 0.1 0.3 0.1 2. Find the mean of the discrete random variable with the probability distribution below. X 3 4 5 6 7 P(x) 0.1 0.2 0.3 0.15 0.25 Page 1 3 I
Question 2 2.1. Let Y,, Y, ., , be a random sample of size 4 from an exponential with parameters and ß = 2 2.1.1. Use the mgf to derive the probability distribution of the sample mean Y. 2.1.2. What is the expected value and the variance of the mean?
If X; and independent, identically distributed (iid) Gaussian random variables with mean, µ, and variance, o², for i € {1, ..., n}, what is the distribution of the sample mean? How is the sample variance related to a common distribution? Sketch the distributions from problem 3 and label key points.
Question 3 The number of accidents which occurs per week on Johnson's Highway follows the Poisson distribution with mean 1.2. A. B. C. Find the probability that: i. ii. The random variable X~ N(25,100). Find: P(X<29) P(23< X<27) No accidents occur in a particular week More than 2 accidents occur in a given week i. 11. 1. 11. Candles are packaged in bags each containing ten candles. A candle is regarded as overweight if it weighs more than 10 grams. The probability that any one candle produced will be underweight is 0.30. A package of candle is selected at random. Calculate the probability, using a binomial distribution that: no candle is overweight exactly THREE (3) candles are overweight
17. Conditional Distributions Consider two random variables X and Y for which we know Pr(X = x) = Pr(X = x|Y = y)for all possible values of x and y. In this case we would say that X and Y are.... Pick ONE option Independent Perfectly correlated Equal to each other More than one of these choices None of these choices
Consider the following joint random variable pmf for X and Y: x y -1 0 1/4 0 1 1/8 1 1 1/2 1 0 1/8 What is the correlation of X and Y?
11.
1. A random variable x has the following distribution. Find the following: a. Missing entry for p(7) b. P(1< x <=4) c. P(3<= x <= 7) d. P(x>2) Using this table find the answers x 1 2 3 4 5 6 7 8 p(x) 0.05 0.10 0.20 0.05 0.10 0.20 0.10
21 0.2 2. Find the variance and the standard deviation of the probability distribution of the random variable X which can take only the values 2, 3, 5, 7, 11, and 13, given that P(2)= 0.15, P(3)= 0.25, P(5)= 0.15, P(7)= 0.10, P(11) = 0.30, and P(13)= 0.05 3. A radio station has six telephone lines. If the host is unable to talk or is talking to another person, the other callers are placed on hold. When all lines are in use, others who are trying to call in get busy signal. The probability that 0, 1, 2, 3 or 4 people will get through is 0.22, 0.10, 0.21, 0.23, and 0.24, respectively. Find the variance and the standard deviation for the distribution. 237
Consider the following probability distribution of the random variable x. 15 20 25 30 f(x) 0.11 0.19 0.31 0.39 Find the variance of the random variable x. Select one: Оа. 25.10 оb. 20.69 O C. 24.90 O d. 24.70 O e. 25.49 O f. 24.10 O g. 26.49 O h. 24.41

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