2. a) Let X and Y be independent identically distributed binomial randomvariables, X~ Bin(3, 0.4) and Y ~ Bin(3, 0.4).i) Compute the probability P(X = 0).ii) Compute the probability that the product XY equals 0, that is,compute P(XY = 0).b) The actual amount of jam (in g) that a filling machine puts into "150 g"jars may be looked upon as a random variable having a normal distribu-tion with σ = 6 and mean μ = 155.What proportion of jars, in the long-run, contain less than 150 g?N(0, 1),Give your answer in terms of the function, where for Z(z) = P(Z), and a give a sketch of the normal curve with a shadedarea that corresponds to the required probability.

Let's solve the provided problems step by step:### 2(a)#### i) Compute the probability \( P(X = 0)…

Answered: 2. a) Let X and Y be independent…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

A X is a normally distributed random variable with u = 25 and o = 5. a) What is the 85th percentile of X? b) What is P(X > 30)? c) What is P(X = 25)?
4. Let X₁ ~ N(0, 3²), X₂ ~ N(4,4²), and X3 ~ N(-1,22) be independent random variables. Find P (X₁ + X₂ + 3X3 < −8), using the table for standard normal distribution.
a.b.c
Suppose R is a discrete random variable that only takes positive integer values. Suppose the cumulative distribution function of R satisfies F(2.5) = 0.6 and F)3.5) = 0.8. Is there enough information to calculate the probability P(R = 3) ? If so, what is the probability?
a) Find the value of the constant C. b) Find the variance of X.
Exercise 4. Let = {a,b,c,d} and define a probability measure on 222 by P(a) = P(c) = 1/6 and P(b) = P(d) = 1/3. Define random variables X and Y by X(a) = X(b) = 2, X(c) = X(d) = −2 Y(a) = Y(d) = -1, Y(b) = Y(c) = 1. (a) List all sets in σ(Y). (b) Let Z = E(XY), determine Z(a) Z(b), Z(c) and Z(d).
23. Let Y denote a geometric random variable with probability of success p. (a) Show that for a positive integer a, P(Y > a) = (1 − p)a (b) Showthatforapositiveintegeraandb,P(Y >a+b|Y >a)=(1−p)a =P(Y >b). (c) Why do you think the property in (b) is called the memoryless property of the geometric distribution? (d) In the development of the distribution of the geometric random variable, we assumed that the experiment consisted of conducting identical and independent trials until the first success was observed. In light of these assumptions, why is the result in part (b) “obvious”? (e) Show that P (Y = an odd integer) = p 1−q2 24. Given that the random variable W is binomial distribution with n trials and success probability p in each trial and P (W = w) = h(w), show that (a) h(w) =p(n−w+1),w>0 h(w − 1) (1 − p)w (b) E [W(W − 1)]= n(n − 1)p2. ? 1 ? 1−(1−p)n+1 (c)E W+1 = (n+1)p
4. Let X₁ N (0,3²), X₂ N(4,4²), and X3 ~ N(-1,22) be independent random variables. Find P (X₁ + X₂ +3X3 <-8), using the table for standard normal distribution.
The random variable X takes values -1, 0, 1 with probabilities 1/8, 3/8, 4/8 respectively. a) Write the CDF of X. b) Write the PMF of Y = X² + 2. %3D c) Compute E(Y).
Suppose that X follows a Binomial distribution, i.e., X ∼ Binomial(3, 0.5). Define a new random variable as Y = X 2 , then, what is the value of the PMF of Y evaluated at 1, i.e., what is Pr(Y=1)? a). 0.3125 b). 0.25 c). 0.375 d). 0.5
2. Some properties of Expected value and variance of a random variable. a) Assume that X is an arbitrary discrete random variable, and a and b are constant. Using the definitic Show: and E(aX + b) = a · E(X) + b V(aX + b) = a² · V(X ) Stat 3128 Ali Mahzarnia P STAT 3128 Ali Mahzarnia b) Justify the computational formula of Variance of a random variable which is to justify : V(X) = E[(X – µ°] = Ex – µ)P • ptx) = | 2: Here needs justification By Cauchy Schwarz inequality it can be shown that the right hand side is always positive. Analogs expression in Mechanic : Parallel axis theorem Iem = I– md² Moment of Moment of inetria about Inertia of an an axis shifted object about the center of a mass by d from center of mass (a parallel shift) Icm is dispersion around the mean and is like second central moment (variance) I is like second moment if d is mean m is like sum total all the weight of each of the x which all add up to 1 d squared is like squared of mean since we,
Pavan

SEE MORE QUESTIONS

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS