Example 3.6.4 Let X have the N(10, 16) distribution (ie. Ganssian distribution with mean 10and variance 16). Find the munerical values of the following probabilities:P{X 2 15), PEX <5), P{X² 2400), and P{X = 2}.

Given X~N(10, 16) Mean=10, variance=16

Answered: Example 3.6.4 Let X have the N(10, 16)…

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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6.4.2
Suppose the random variable X has a geometric distribution with p = 0.4. Determine the following probabilities: (a) P(X = 2) = i (b) P(X = 4) = i (c) P(X = 8) = i (d) P(Xs 2) = i (e) P(X > 2) = i Round your answers to four decimal places (e.g. 98.7654).
5.1.7 Five males with an X-linked genetio disorder have one child each. The random variable x is the number of children among the five who inherit the X-linked genetic disorder. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied. PO O 0.033 0.157 2 0310 3. 0.310 4. 0.157 0.033 Does the table show a probabilty distribution? Select all that apply A. Yes, the table shows a probability distribution. B. No, not every probab tyis between 0 and 1.inclusive. No, the random variable Xs numbervalues are not 355ociated with probablities No. the random varable xis categorcalinstead of numerical. No the sum of all the probablities is not equaltto 1. Cick to select your answerS) and tren cexCheckAnSwer
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
3.6.2 Suppose X is a negative binomial random variable with p=0.2, r=4. Find: a. E(X) b. P(X=20) c. Most likely value for X
2. Assume a discrete random variable X follows a discrete distribution, where the possible values of X are 0, 2, 4, 6, with the corresponding probabilities 0.3, 0.2, 0.2, and 0.3, respectively. Generate a sample of 10000 values from the given discrete distribution and see how close the sample mean and standard deviation to the theoretical values. 3. Let random variable y follows a binomial distribution, Binomial (8, 0.5). a) Calculate P(Y=5) b) Calculate P(Y6). c) Draw 50,000 samples from this binomial distribution and draw a bar plot.
5.3.6 Given a normally distributed population with a mean of 100 and a standard deviation of 20, find the following probabilities based on a sample of size 16: (a) Pð"x ! 100Þ (b) Pð"x 110Þ (c)Pð96 "x 108Þ
Suppose that the weights of people who work in an office building are normally distributed with a mean of u = 165 Ib. and a standard deviation of o = 25 lb. What is the chance that the total weight of 5 people is more than 1000 Ibs., i.e., what is P(X1+ ... + X5 > 1000)? [Hint: try to express this as an X-style problem.
14) Xi -2 -1 0 1 Consider the following probability distribution. The variance is A) 1.14 B) 1.29 C) 1.65 D) 1.94 P(X = X₁) 0.2 0.1 0.3 0.4
Assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.25 probability that a pea has green pods. Assume that the offspring peas are randomly selected in groups of 36. Complete part (a) through (c) below. ..... a. Find the mean and the standard deviation for the numbers of peas with green pods in the groups of 36. The value of the mean is u = рeas. (Type an integer or a decimal. Do not round.)
Compute the expected value of x+y.

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Example 3.6.4 Let X have the N(10, 16) distribution (i.c. Ganssian distribution with mean 10 and variance 16). Find the munerical values of the following probabilities: P{X215), P{X <5). P{X² > 400), and P{X = 2}.