1. Suppose we have the experiment of forming random binary code consisting of 4characters. Let X be a discrete random variable representing the number of ones.a. Determine the pmf and CDF of X. Plot these functions.b. Find F(0) and F(2). Interpret.c. Compute P(1 < X < 2) and P(X> 3).

(a) A probability mass function or pmf is a function over the sample space of a discrete random…

Answered: 1. Suppose we have the experiment of…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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ZV. O *** 0004 : l 36 l ZAIN IQ Asiacell رسالة 1 غير مقروءة Question 1 There are two boxes the first box contains 3 red beads and the second box contains 2 red beads and 3 black beads we select a random bead from the first box and put it on the second box then we take out 2 random beads without replacement. If the random variable x is equal to the number of red beads from the second box A.find the probability function of x B.find p(0
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Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(Y)=-7 Var (X) = 20 Var (Y)=6 Var (z) = 23 E (X) = 5 E(Z) = 3 Compute the values of the expressions below. E (-2X – 4) = -3Z + 2X E 3 Var (27 + 3) - O =(-sx") - O
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(X)=5 Var(X) = 44 Var(Y)=23 Var(Z) = 32 E (Y)=-2 E(Z)=-4 %3D %3D Compute the values of the expressions below. E(-5+5Y)= | 3Y+5X E -3 Var(5X-5) = I E-2
A QR code photographed in poor lighting, so that it can be difficult to distinguish black and white pixels. The gray color (X) in each pixel is therefore coded on a scale from 0 (white) to 100 (black). The true pixel value (without shadow) the code is Y = 0 for white, and Y = 1 for black. We treat X and Y as random variables. For the highlighted pixel in the figure is the gray color X = 20 and the true pixel value is white, i.e. Y = 0. We assume that QR codes are designed so that, on average, there are as many white as black pixels, which means that pY (0) = pY (1) = 1/2. In this situation, X is continuously distributed (0 ≤ X ≤ 100) and Y is discretely distributed, but we can still think about the simultaneous distribution of X and Y. We start by defining the conditional density of X, given the value of Y : fX|Y(x|0) = "Pixel is really white" fX|Y(x|1) =" Pixel is really balck " Use Bayes formula as given in the picture and find the probability for x = 20 like in the picture.
7) Suppose that X and Y are two independent measurements. We can treat these measurements as random variables, where X has the mean of 1 and standard deviation of 2, and Y has the mean of 2 and the standard deviation of 3. For the transformations below, find the mean, variance, and the standard deviation. a) X+Y b) X-Y c) 2X+Y d) X-2Y+1
The data shown to the right are from independent simple random samples from three populations. Use these data to complete parts (a) through (d). Sample 1| Sample 2| Sample 30 E Click the icon to view a table of values of Fa- 4 5 2 6 14 a. Compute ST, SSTR, and SE using the following computing formulas, where x, is the ith observation, n is the total number of observations, n; is the sample size for population j, and T; is the sum of the sample data from population j. SST = Ex? - (Ex)? /n, SSTR= E(T? /n) - (Ex)? /n, and SSE = SST-SSTR Compute the values required to find SST, SSTR, and SSE. n= Ex = Ex = E(T; /n) = (Type integers or decimals. Do not round.) Calculate SST, SSTR, and SSE using the computing formulas. SST = (Type an integer or a decimal. Do not round.) SSTR= (Type an integer or a decimal. Do not round.) SSE = (Type an integer or a decimal. Do not round.) b. Compare your results in part (a) for SSTR and SSE with the following results from the defining formulas. SSTR = En (x…
The degrees of freedom (df) for the One Sample t test and the Independent Sample t test are _________. a. One Sample t test: N-1 Independent Samples t test: N-1 b. One Sample t test: N Independent Samples t test: N-1 c. One Sample t test: N-1 Independent Samples t test: N-2 d. One Sample t test: N-2 Independent Samples t test: N-1
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Let X,, X2, and X3 be independent random variables, each are binomially distributed with n = 100 and p = 0.2. Let A = X,– 2X2 and B = X3 + 3X1. Find PAB- %3D %3D
Let (S, P) be the sample space with S = (1, 2, 3, ..., 10) and P (a) = 1/10 for all a ES. For this sample space, define the random variables X and Y by #2. X(s) = 25 and Y(s) = s a. Evaluate P (X< 10). b. Evaluate P (Y < 10).
The table below shows the number of male and female students enrolled in nursing at a university for a certain semester. A student is selected at random. Complete parts (a) through k (d). Males Females Total Nursing majors 93 700 793 Non-nursing majors 1015 1723 2738 Part 3 of 4 Total 1108 2423 3531 P(not being female or being a nursing major) = (Round to the nearest thousandth as needed.). (a) Find the probability that the student is male or a nursing major. P(being male or being nursing major) = 0.512 (Round to the nearest thousandth as needed.) (b) Find the probability that the student is female or not a nursing major. D P(being female or not being a nursing major) = 0.974 (Round to the nearest thousandth as needed.) (c) Find the probability that the student is not female or a nursing major. H C n 101 √₁ Vi L (0,0) 4 x

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1. Suppose we have the experiment of forming random binary code consisting of 4 characters. Let X be a discrete random variable representing the number of ones. a. Determine the pmf and CDF of X. Plot these functions. b. Find F(0) and F(2). Interpret. c. Compute P(1 < x≤ 2) and P(X> 3).