Two random variables have expected values E[X] = 0.6 and E[Y] = 0.2 and E[XY] = 1.2. Are X and Y independent random variables? O No Yes

Q: 4, ii. a probability distribution function m(x) for a discrete random variable X such that a…

A: We have to find PMF of a discrete random variable X with mean and standard deviation such that

Q: Previously, you studied linear combinations of independent random variables. What happens if the…

A: Since,

Q: 4. The continuous random variable X has a lognormal distribution if the random variable Y = In(X)…

A: import numpy as np sample = np.array([5.75, 5.73, 5.57, 5.67, 5.42, 6.02, 5.85, 5.39, 5.50, 5.37,…

Q: Let N be the last digit of your student number. Let X and Y be two continuous random variables that…

A:

Q: Let X1, X2, X3 be i.i.d. random variables N(0, 1). Show that Y1 = X1+8X3 and Y2 = X2+8X3 have…

A: Solution:         ut   x1    x2 , x3    iid ~N(u=0, α2=1)         ut  Y1 = x1 +δ x3 & y2= x2+δx3…

Q: Find the expected value for the random variable

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Q: d. Let X and Y be independent normal random variables, each with mean u and standard deviation o. 1.…

A:

Q: Q3. The moment generating function for a random variable X is e3t M(t)=1-t2¹ What are the mean and…

A: The moment generating functionMx(t)=e3t/(1-t2)    -1<t<1To find mean and variance of X Concept…

Q: 1. The random variable X has probability distribution. X 1 3 5 7 9. P(X=x) 0.2 0.2 0.15 Given E(x)=…

A:

Q: A toll road charges $4 for passenger cars and $7 for other vehicles. Let X1 be the number of…

A:

Q: We have a random variable X1 defined on Population 1.  X1 has a mean value of 52 with a population…

A: Given that the expectation of random variable X1 and X2 are EX1=52 and EX2=50, respectively and…

Q: ru+1.50/VR 1-1.20/VE()*dr.

A: As per bartleby guideline if more than one question asked, only first question to be answered.…

Q: 4

A: The value of mean is given as, Ex=1.5. The value of variance is given as, varx=0.25. To determine…

Q: Let X and Y be independent random variables such that E(X)=2, E(Y)=2, var(X)=2, and var(Y)=2…

A: We know that, If X and Y are independent random variables.  Var(X+Y)= Var(X)+ Var(Y)

Q: Given Y it = B 0 + B 1Treated i + B2After t + B3(Treated i*After t) + e it, the expected value of…

A: Given information: The given regression equation is as given below:

Q: 3. V, W, X and Y are independent random variables, each having a normal distribution. V has mean 4…

A:

Q: 7. Suppose X and Y are independent random variables. Y a. What is the correlation coefficient of X…

A: X and Y are independent random variable. So, Cov(X,Y) = 0 a. We need to find the correlation…

Q: 3. Let X and Y be two Binary random variables with joint probability distribution: x = 0 x = 1 0.2…

A: The joint probability density function is given as- fx,y x=0 x=1 y=0 0.2 0.4 y=1 0.1 0.3

Q: (1 point) Consider the following table: X Pr Product 0 0.2 10 0.6 а 0.5 2.5 5 6 с 1. What are the…

A: 1. The value of a is 0.2, the value of b is 0.1 and the value of c is 0.6. The condition for…

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!