Let the random variable X represent the number of purple marbles selected when a group of 4 marbles are selected from 20 marbles, of which 8 are purple, 6 are sky blue, and6 are whiteThe probability mass function X is given below.XexPIX=x)495/484511760/4845a) Find the mean u, or expected value of the variable Xb) Find the variance of and standard devitation a for the random variable X21848/48453672/4845470/4845

It is required to obtain the expected value, variance, and standard deviation of the random variable…

Answered: Let the random variable X represent the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Two boxes each contain three cards. The first box contains cards labelled 1,3 and 5; the second box contains cards labelled 2,6 and 8. In a game, a player draws one card at random from each box and his score ,is the sum of the numbers on the two cards(i) Obtain the probability distribution for the random variable X(ii) Calculate E[X ], E[X^2] and variance of X(iii) Calculate the median and mode of X
Let x be a random variable that represents the pH of CVS brand water. The mean of this x distribution is µ = 6.5 pH. A new company wants to sell its water at CVS locations. However, CVS management believes that the new brand will have a mean pH less than the CVS brand water. A random sample of 50 water samples were taken from this new company's water and it was found that the sample mean was 6.3 pH and the sample standard deviation was s = 0.5 pH. Do the data indicate that the new company's water has a mean pH level less than 6.5, which is the pH of the CVS brand water. Use a 5% significance level. Identify the following in your answer. 1. Identify the null Ho and alternative hypotheses H1 for the problem. 2. Identify the following: Sample statistic • Test Statistic (t): (Round to three decimal places) p - value: (Round to four places) • Calculator key used. 3. Identify the significance level and determine if you reject or fail to reject the null hypothesis. 4. State your conclusion.
The weights of beagles (dogs) have approximately a normal distribution with u = 17.1 pounds and a standard deviation of o = 1.8 pounds. Suppose that we randomly select n = 64 beagles and measure their weights in pounds. Let X be the random variable representing the mean weight of the selected beagles. Let Xtot be the random variable representing the total weight of the selected beagles. a) About what proportion of beagles have weights between 17 and 18 pounds? b) About what proportion of beagles have weights greater 20 pounds? c) About how many of the 64 sampled beagles have weights less than 16.5 pounds? (nearest integer) d) About how many of the sampled beagles have weights between 17 and 18 pounds? (nearest integer) e) What is the standard deviation of the distribution of X? f) What is the standard deviation of the distribution of Xtot? g) What is the probability that 17 1100? f) Copy your R script for the above into the text box here.
Prob and stat
Let X1, X2, X3… X20 be a random sample from a distribution with mean 8 and variance 5. Find the mean and variance of .
Need help with 8 d and e please
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
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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