1. Let \( X \) be a continuous random variable with cumulative distribution function (cdf)\[F(x) = \begin{cases} 0, & x \leq 0 \\\frac{x^2}{4}, & 0 \leq x < 2 \\1, & 2 \leq x\end{cases}\]a. Find \( P(X \leq 1) \), \( P(1 \leq X \leq 1.5) \), and \( P(X > 1.5) \).b. Derive the probability density function (pdf) of \( X \).c. Find the median and 75th percentile of the random variable.

Answered: Image /qna-images/answer/89f2fe93-5cbf-4f82-8a56-21bbf8648d5f.jpg

Answered: 1. Let X be a continuous 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

See similar textbooks

Similar questions

please answer??
1
Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)
Let random sample of n observations from each of the distributions: a. Poisson distribution with parameter θ. b. f(x, θ) = (1/ θ) e-x/θ , 0 < x. In each case find the Minimum Variance Estimator of θ and prove its efficiency.
25. Let X have a three-dimensional normal distribution with mean vector and covariance matrix and A- 3-1 respectively. Set Y= X1 +X + X, and Y= X1+X. Determine the conditional distribution of Y given that Y 0.
2. The random variable X is the amount of fructose in apples (in ounces) grown at a local orchard and is represented by the following cdf: 2(x +), 1
time, i.e. P(μx-ox ≤ x ≤ μx + 0x). 3. Suppose that people heights are normally distributed with mean of 170 cm and standard deviation of 6 cm. a) What proportion of people are between 165 cm and 175 cm tall? b) Find the minimum ceiling of an airplane such that at most 5% of people walking down the aisle will have to duck. E c) Find the probability that the average height of a random sample of 49 people is greater than 172 cm. 80 F3 4 R % 5 T F6 Y 1 & 7 K ard deviation of the expected U 8 DII
The probability function of a continuous random variable, X, is given by the equation: fx(x) = 0.0064x(25-x²) for 0 < X < 5 Draw plots of both the pdf and the cdf of X.
Let Y1,..., Y, be i.i.d. random variables from the Weibull distribution f(y; 0) Σ (멤) exp ), y > 0. Show that ô = Li=1í is an unbiased estimator of 0. Is Ô an efficient estimaotr of 0?
Compute the ff.: Expected Value of X ~ N(0, 1) Variance of X ~ N(0, 1) Moment Generating function of X ~ N(0, 1)
The random variable x has a normal distribution with mean 50 and variance 9. Find the value of x, call it x0, such that: a) P(x ≤ xo) = 0.8413 b) P(x > xo) = 0.025 c) P(x > xo) = 0.95 d) P(41 ≤ x ≤ xo) = 0.8630
The time to wait between each phonecall a person recives is random given f(t) = 3e-3t for t>=0. Let T1 and T2 be two independent waiting times for this distribution. Find expected time between each call and variance. (E(T) and V(T)) Find the probability for both T1 and T2 to be greater than one.

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

1. Let X be a continuous random variable with cdf 0, x≤0 x² F(x)= = 7,0 ≤ x < 2 1, 2≤x a. Find P(X ≤ 1), P(1 ≤X ≤ 1.5) and P(X>1.5). b. Derive the pdf of X. c. Find the median and 75th percentile of the random variable.