For a discrete random variable X if: * (2 Points) P (X = x) = 0.1x ,x = 2, 3, 5, then E (X²) = %3D %3D

Q: Suppose a continuous random variable X has the following CDF::  F(x) = 1 - 1/ (x+1)4, x > 0. Find SX…

A: We have given, A continuous random variable X has the following CDF: F(x) = 1 - 1x+14, x > 0.

Q: If X and Y are independent random variables with variances Var(X) = 5 and Var(Y)= (a) find the…

A: Given  V(x)=5, V(y)=3,  Z=-2x+4y-3  X and Y are independent

Q: 1- P(Y > 1) 2- P(X>2|Y< -1) 3- P (3<X<7)

A:

Q: The profit for a new product is given by Z= 3X- Y- 5. If X and Y are independent random variables…

A: Answer - Given, Z = 3X - Y - 5             X and Y are independent random variables  with σx = 1…

Q: la) P(X>2) (b) P (Y > 0), where Y = - 2

A: given  X~N5,2  the  z=X-μσ~N0, 1    mean = 5     variance = 2      ,   a) PX &gt;2=PX-μσ&gt;2-52…

Q: Question 8. Let X and Y be random variables with Var(X) 1, Var(Y) 3, and Var(X-Y)3D4. The…

A: Solution: From the given information,

Q: Let X1, X2, X3, X4 be independent random variables of size 4 from a gamma distribution G(a, X) = -1…

A: We want to find the variance of Xi

Q: 3. Let X1 and X2 be uncorrelated random variables. Let Y₁ = X₁ + X2 and Y2 = X1 - X2. (a) Find…

A: and  are uncorrelated random variables.

Q: 2)Consider a random variable X with MGF M(t) = e³t+4t² Find the mean and variance of X.

A: Question 2)The moment generating function (MGF) of a random variable  is, The objective is to…

Q: 4. Let X be a discrete random variable with E (X) = 3 and Var(X) = 0.5, What are the mean and…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: lom variable X is given below. fx(x) 1 2 a random variable Y, where whose PDF is given below. fy(y)

A: *Answer:

Q: Suppose Y₁, Y2,,Y,, is an iid sample from a beta (a, 3) distribution with a 3-0, 0>0 a. Use the…

A: Given:Y1,Y2,.....,Yn is an iid sample from a Beta(α,ß)α=ß=θ,    θ&gt;0Find:a)Show that the given T…

Q: 6. Two independent random variables X1=(-1,0,1) and X2=(-1.0) can take the following probability…

A: Expected value is also known as mean or average. It used to take average for discrete or continuous…

Q: 3(8x-x) Determine the mean and variance of the random variable for f(x)% = 0<x<4. 128 Round your…

A: Given f(x)=3(8x-x2)128 ; 0&lt;x&lt;4

Q: If X₁, X₂, X3, .., Xn are random sample from a population with mean μ and variance o², then what is…

A: Given that X1,X2,...,Xn is a random sample from a population with mean μ and variance σ2 and…

Q: m varia bies 10, 0x2 correlation between 'U' and 'V' is zero, when U = 3 X + 4 Y and V = 3 X- Y.

A:

Q: For any two random variables Y₁ and Y₂, Var(Y₁Y₂|Y₁ = y₁) = y{Var(Y₂|Y₁ = y₁). TRUE

A: Given that Y1 and Y2 are two random variables. Formula: If X is a random variable, then VX=EX2-EX2.…

Q: Let X be a random variable. (a) Let YaX be another random variable. What is EY, in terms of μ = EX?…

A: Given : X be the random variable  Y=aX

Q: The cdf of a random variable Y is |1– exp(-0.4y), y 20 F,(y) otherwise Valuate P{2.5 <Y < 6.2}.

A:

Q: A random variable X has P(5<X<19) 2 0.75. Using Chebyshev's theorem, the mean and variance (H, o2)…

A: The mean will be the average of 5 and 19. So, mean= (5+19)/2=12

Q: Suppose x is a normally distributed random variable with u = 31 and o = 6. Find a value xo of the…

A:

Q: Given that X and Y are independent random variables and E(x) = 4, E(Y) = 7, Var(x) = 3, Var(Y) = 6;…

A: x and y are independent events. E(X) = 4 E(Y) = 7 Var(X) = 3 Var(Y) = 6   Var(X-6) = ?

Q: For a random variable X , suppose that E[X] = 3 and Var(X) = 4. Then (a) E[(5+X)^2]=   (b) Var (2…

A: For a random variable X , suppose that E[X] = 3 and Var(X) = 4. Then (a) E[(5+X)^2]=   (b) Var (2 +…

Q: Suppose that the random variables X and Y are independent with Var(X)=8 and Var(Y)=6. Calculate…

A: Given Data: Var(X)=8 Var(Y)=6

Q: X and Y are random variables that are both Normally Distributed. The Mean of X is 5 and its SD is 3.…

A: Given that  P(4 &lt; Y &lt; 16) = P(A &lt; X &lt; B) μX=5σX=3μY=-2σY=6

Q: (a) (b) Find E(W). Find Var(W).

A: Given,let  be  independent random variables.E(Yi)=μ and Var(Yi)=σ2  for every since (a)we want to…

Q: Let X be a random variable taking only the values 0, 1, 2, 3, 4 with probabilities given by P(X = 0)…

A: Discrete probabilty  The conditions of the probability is 1) p(x) ≥ 0 2) Σp(x)=1

Q: A noisy resistor presents a voltage X distributed as a Gaussian random variable with zero mean and…

A: X : voltage of a noisy resistor    Therefore,  X ~ N(mean : μ = 0, standard deviation : σ = 2 =…

Q: Let X, and X be two identically distributed random variables with a correlation coefficient equal to…

A: First, we need to find the covariance of X1  and X2 from their correlation coefficient,

Q: Suppose a discrete random variable X takes only three values 0, 2 and 3. If P(0)=0.5, P(2)=0.2 and…

A: For a Discrete Random Variable X where X takes only three values that is 0,2 and 3 P(0)=0.5 ,…

Q: (TRUE / FALSE) For two random variables, X and Y , E(XY ) = E(X)E(Y ) if X and Y are uncorrelated.

A: Solution: The covariance between the random variable X and Y can be defined as  Cov(X,Y)= E(XY)-…

Q: If X is a continuous random variable that takes on values between 10 and 40, then the P(X = 15.5) =…

A: We have given that  X is a continuous random variable that takes on values between 10 and 40, then…

Q: 2. A random variable X has only two values a and b with P(X = a) = p , P(X = b) = q (p+q = 1). Find…

A: Let X be a random variable with the values a and b. The probability distribution table is…

Q: Let X and Y be two random variables with E (X) = 1, E (Y) = 2, Var (X) = 1, Var (Y) = 2, !! Cov (X,…

A: Given that the mean of aX+bY is 3  So,  E(aX+bY)=3aE(X)+bE(Y)=3a(1)+b(2)=3a+2b=3a=3-2b ..........(Eq…

Q: 1) If Var(X-Y) = 2, Var(X+ Y) = 4, E(X) = 3 and E(Y) E(XY)? = 1, than what is

A: According to bartleby experts guidelines we can answer only question. Rest can be repost.

Q: Find: (f(x\y = 4)

A: Here construct joint probability distribution table from given information

Q: fx(x) 4 a -1a

A: We have to find the value of constant for valid pdf.

Q: Let X and Y be two random variables. Suppose we know E(X) = 7 and E(Y)=3. Let Z = X − Y be a random…

A: Given EX=7 and EY=3.Let Z=X-Y.Then,E(Z)=4

Q: Let y be a normally-distributed random variable with mean u= 100 and variance 2 = 16: Select which…

A: We know If random variable X ~ N(a, b2) where mean(x) = a, standard deviation(x) = b.  then,  P(a-b…

Q: 2x + 1 25 b. P(X ≤ 1) d. P(X> -10) 3.1.11 WP SS a. P(X= 4) c. P(2 ≤X <4) vs f(x) = x = 0, 1, 2, 3, 4

A:

Q: Suppose that X is a random variable for which the m.g.f. is as follows: M(t) = 1/4(3et+e-t), -∞<t<∞…

A: We can get the mean and variance after finding the first and second derivative of mgf at t= 0

Q: X is a random variable with distribution X 1 P(x) 0.4 0.6 X1 and X2 are two random variables and…

A: The following information is given in the question X 0 1 P(x) 0.4 0.6 Now, Since X1 and X2…

Q: a prob. 174 Find (c) E (XY)

A:

Q: = 1- Q(x).

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.