2. Consider the following probability distribution:.4-1024p(x) 0.020.07 0.10 0.15 0.300.180.10 0.06 0.02a) Calculate μ,02, and σb) Graph p(x). Locate μμ-2, and μ + 2σ on the graph. Ic) What is the probability the x is in the interval μ 2a?

a.Find the mean of the variable X using the given probability distribution.Mean:The general formula…

Answered: 2. Consider the following probability…

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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1. Let X be the mean of a random sample of size n = 64 from the exponential distribution e-2/², x>0 otherwise 0, f(x)= = Based on central limit theorem, approximate the probability P (1.8 < X < 2.1). Round your final answer to 4 decimals.
9. Find the probability of z occurring in the indicated region. J 0 1.75
The following six graphs correspond to three probability density functions and their cu- mulative distribution functions, but they are all mixed up. 0.8 1.5 0.6 A. В. 0.4 0.5 0.2 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1 1.5 0.8 0.6 C. D. 0.4- 0.5 0.2 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1 0.8 0.6 E. F. 2 0.4 0.2 0.2 0.4 0.6 0.8 0.2 0.4 0,6 0.8 Identify the graphs for each of the three probability density functions (PDFS), in alphabetical order. For each PDF, indicate which graph represents the corresponding cumulative distribution funetion (CDF). PDF CDF
a. b. Let X have a gamma distribution with a=2 and 3-2. What is P(X>2)? Let X have a log-normal distribution with u-3.5 and o=1.2. Find P(50
state s probability P(s) realization X(s) realization Y(s) 1 .1 10 20 2 .2 20 30 3 .2 10 10 4 .3 10 30 5 .1 20 10 6 .1 30 20 What is E(Y|X = 20)? a) 65/3 b) 70/3 c) 25 d) 80/3
ymbol) message X asuming that the symbols ICAIE oy P Qi b) Telegraph system has two symbols (dot, dash), assume time of the dot symbol equal 0.2 sec and the time of dash symbol equal 0.4 sec, Probabilities are P(dot)-2/3 and P(dash)-1/3.Calculate Hass D g1 Entropy rate? (2:245
Given the probability distributions for variables X and Y shown to the right, compute the terms below a. E(X) and E(Y) b. ox and dy C. OXY d. E(X+Y) P(X,Y) 0.4 0.6 X 100 300 Y 300 100 0
Suppose X and Y have the following joint distribution: (please refer to image attached) Find the distributions of X and Y. Find Cov (X, Y), i.e. the covariance of X and Y. Find p(X, Y), i.e. the correlation of X and Y.
For numbers 2 to 4: Below is the probability distribution of the number of calls received by a switchboard operator within a one-hour interval, X. X = x 2 3 4 5 6 P[X = x] 0.13 0.27 0.27 0.18 0.04 0.02 2. What is the probability that at most 4 calls are received by the switchboard operator within one hour interval? O A. 0.06 B. 0.09 O C. 0.94 D. 1.00
5.2.1 The conditional probability distribution of Y given X = x is fy.0) = xe-y for y> 0, and the marginal probability distribution of X is a continuous uniform distribution over 0 to 10. a. Graph fyv) = xe¬w for y > 0 for several values of x. Determine: b. P(Y < 2|X = 2) d. E(Y |X = x) f. fr(y) c. E(Y | X = 2) e. fxy(x, y)
The graph of the discrete probability to the right represents the number of live births by a mother 42 to 46 years old who had a live birth in 2015. Complete parts (a) through (d) below. 0.30 0-279 0.25 0.238 0,20- U.168 0.15 15 0.097 0.10 0.05 004 0036 0.043 0.00- 1 2 3 8 Number of Liive Births (a) What is the probability that a randomly selected 42- to 46-year-old mother who had a live birth in 2015 has had her fourth live birth in that year? 0.112 (Type an integer or a decimal.) (b) What is the probability that a randomly selected 42- to 46-year-old mother who had a live birth in 2015 has had her fourth or fifth live birth in that year? 0.206 (Type an integer or a decimal.) (c) What is the probability that a randomly selected 42- to 46-year-old mother who had a live birth in 2015 has had her sixth or more live birth in that year? 0.101 (Type an integer or a decimal.) hp esc & 8

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2. Consider the following probability distribution: .4 -1 0 2 4 p(x) 0.020.07 0.10 0.15 0.300.180.10 0.06 0.02 a) Calculate μ,02, and σ b) Graph p(x). Locate μμ-2, and μ + 2σ on the graph. I c) What is the probability the x is in the interval μ 2a?