Problem #5Draw a county at random from the state of Maryland.Then, draw n people at random from the county. Let X be the number of thosepeople who have tested positive for COVID-19. If Q denotes the proportion ofpeople in that county with COVID-19, then Q is also a random variable since itvaries from county to county. Given Q = q, we have that X - Binomial(n, q).Thus, E(X |Q = q) = nq and Var( X | Q = q) = nq(1-q). Suppose that the randomvariable Q has a Uniform(0, 1) distribution. A distribution that is constructed instages like this is called a hierarchical model and can be written asQ ~ Uniform(0, 1)X|Q = q~ Binomial(n, q).Then, find E(X) and Var(X).

We have to find the expectation and variance of random variable X using conditional expectation and variance.

Answered: Problem #5 Draw a county at random from…

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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These questions concerns the following situation. There is a rain on a football ground. The ground is 100 meters long and 70 meters wide. Model the event of a raindrop falling as a randomly selected point in the rectangle pictured.Lets imagine the following random variables: X is the x-coordinate where a raindrop falls, Y is the y-coordinate of where a raindrop falls, and Z=X+Y. CHOOSE ONE AND SHOW THE PROCESS. Which one of the following statements are true? * a) X and Y are independent b) X and Z are independent c) Y and Z are independent
Previously, you studied linear combinations of independent random variables. What happens if the variables are not independent? A lot of mathematics can be used to prove the following: Let x and y be random variables with means ?x and ?y, variances ?2x and ?2y, and population correlation coefficient ? (the Greek letter rho). Let a and b be any constants and let w = ax + by for the following formula. μw = aμx + bμyσ2w = a2σ2x + b2σ2y + 2abσxσyρ In this formula, r is the population correlation coefficient, theoretically computed using the population of all (x, y) data pairs. The expression ?x?y? is called the covariance of x and y. If x and y are independent, then ? = 0 and the formula for ?2w reduces to the appropriate formula for independent variables. In most real-world applications the population parameters are not known, so we use sample estimates with the understanding that our conclusions are also estimates.Do you have to be rich to invest in bonds and real estate? No, mutual fund…
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The answer is 23
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.
Q.no.4 The test scores on the same algebra test were recorded for nine students randomly selected from a classroom taught by teacher A and eight students randomly selected from a classroom taught by Teacher B. Teacher A: 65, 88, 93, 95, 80, 76, 79, 77.Teacher B: 91, 85, 70, 82, 92, 68, 86, 87, 75. Test the hypothesis that the difference in the average scores for students taught by these two teachers equal to zero. Use 5% level of significance.
Problem 12 Let X and Y be two independent random variables with PMFS for x = 1, 2, 3, 4, 5 Px(k) = Py(k) = %3| otherwise Define Z = X – Y. Find the PMF of Z.
If a random variable X is defined such that: E[(X - 2)²] = 18 and E[(X+1)²] = 33. Then the values of u and o are: %3D %3D u = 3 and o = V17 u = 6 and o = 3 and o=32 3/5 and o=6
3. An integer is randomly chosen from the set 1, 2,..., 100. If this integer is divisible by 2 we let Y = 0, and if it is not divisible by 2 but is divisible by 3 then Y = 1. We let Y = 2 in all other cases. Find mean and variance of Y.
In Mendel's experiment, he obtained 724 plants with red flowers and 210 with white flowers in his cross of red flowered x white flowered pea plants. Is this result consistent with his hypothesis of factor segregation? Calculate the x and obtain the approximate value of P from Table 1, then interpret the results and clearly state your conclusion. Table 1: Chi-square table Chi Square Values and Probability Degrees of Freedom P= 0.99 0.95 0.80 0.50 0.20 0.05 0.01 1 0.000157 0.00393 0.0642 0.455 1.642 3.841 6.635 2 0.020 0.103 0.446 1.386 3.219 5.991 9.210 3. 0.115 0.352 1.005 2.366 4.642 7.815 11.345 0.297 0.711 1.649 3.357 5.989 9.488 13.277
Here is one way to think about a mixed random variable. Suppose that we have a discrete random variable Xa with (generalized) PDF and CDF fa(r) and Fa(x), and a continuous random variable X. with PDF and CDF f.(r) and F.(x). Now we create a new random variable X in the following way. We have a coin with P(H) = p. We toss the coin once. If it lands heads, then the value of X is determined according to the probability distribution of X4. If the coin lands tails, the value of X is determined according to the probability distribution of Xe. a. Find the CDF of X, Fx(x). b. Find the PDF of X, fx(x). c. Find EX.
Q.No.3. Solve the followings:i. How many groups of 5 people can you form from 10 people?ii. Can a random variable have negative output? Prove it

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