3) A discrete random variable X has the following probability distribution:12345.7P(X)K2K2KЗКK22K27K2+KFind the value of K. Also find the mean and variance of the distribution.

We want to find k, mean and variance.

Answered: 3) A discrete random variable X has the…

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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The probability distribution of the discrete random variable X is 3-х 3y x = 0,1,2,3. Find the variance of X.
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.
Q4: The probability mass function of a discrete random variable X is given by the following table: X 1 2 3 4 5 6 P(X) 1/36 3/36 5/36 7/36 9/36 11/36 Find 1- Cumulative distribution function. 2- Draw a graph of the probability mass function and cumulative distribution function. 3- Mean and variance. 4- Standard deviation.
Q4: The probability mass function of a discrete random variable X is given by the following table: X 1 2 3 4 5 6 P(X) 1/36 3/36 5/36 7/36 9/36 11/36 Find 1- Cumulative distribution function. 2- Draw a graph of the probability mass function and cumulative distribution function. 3- Mean and variance. 4- Standard deviation.
Q2: A random variable X has a mean = 8, a variance o² = 9, and an unknown probability distribution. Find P(X-826).
Suppose you were given this Joint Probability Distribution: x=number of bars of signal strength x=number of bars of signal strength x=number of bars of signal strength x=number of bars of signal strength y=number of times city name is stated 1 2 3 Marginal probability distribution of y 4 0.15 0.1 0.05 0.3 3 0.02 0.1 0.05 0.17 2 0.02 0.03 0.2 0.25 1 0.01 0.02 0.25 0.28 0.2 0.25 0.55 Marginal probability distribution of x Marginal probability distribution of x Marginal probability distribution of x Marginal probability distribution of x Find the conditional mean and variance of Y|3 Mean = Variance =
9
There are two independent random variables X and Y. X has mean 4 and standard deviation , and Y also has mean 4 and standard deviation . A random variable W is the difference between X and Y. That is, W = X - Y. Calculate the mean of W.
Soledad and Tania are both high school students. The number of texts Soledad sends daily, S, is approximately Normally distributed with a mean of 100 and a standard deviation of 6 texts. The number of texts Tania sends daily, T, is approximately Normally distributed with a mean of 108 and a standard deviation of 8.1 texts. Assume that S and T are independent random variables. Let D = S – T. What is the probability that Soledad sends more texts on a randomly selected day? 0.104 0.214 0.786 0.896
Let X and Y be 2 random variables with joint probability distribution given in the following table: f(x,y) 1 3 0.3 0.2 Y 4 0.1 0.4 Then f(Y = 3|X = 0) is equal to: a. 0 b. 0.5 c. 0.75 d. 1
3. Table 1 below shows the probability distribution of hurricanes that have made landfall in the Caribbean. The random variable, X, is the category of the hurricane. Category 1 is the weakest hurricane level while category 5 is the strongest. Table 1 x 1 2 3 4 5 P(X=x) 0.41 0.34 0.13 0.07 * a) Find the value of ‘*’. [1] b) Find the expected category of hurricane to make landfall, E(X). [2] c) What is the probability that a Category 4 or stronger hurricane will make landfall?[1] d) Calculate the variance. [3]

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3) A discrete random variable X has the following probability distribution: 1 2 4 6. 7 P(X) K 2K 2K 3K K2 2K2 7K2+K Find the value of K. Also find the mean and variance of the distribution.