(iiven that A and B are two independent events such thatP(1) = 46. andP(A U B) P(B) = 10 2 13

Q: 2] If a random variable X is defined such that E[(X - 1)2]=10 ,E[(X- 2)²]=6. find u and o?. | =

A:

Q: Suppose X, Y are two discrete random variables with probability function given by: Y X 1/9 1/9 -1 1…

A: There are two type of variable, they are dependent and independent variable. Dependent variable is…

Q: Suppose X, Y are two discrete random variables with probability function given by: Y X-1 1/8 1/8 1/8…

A: Multiplication of marginal probabilities are are compared with joint pmf.

Q: Suppose X is a discrete random variable with finite first and second moments. Show that E (x…

A: It is given that X is a discrete random variable with finite first and second moment.

Q: Suppose the c.d.f. of random variable X is defined as if x 2

A:

Q: If A and B are events such that ​P(A)equals=0.60 and P(A∪​B)equals=0.70​, find​ P(B) when ​(a) A…

A: (a)If events A and B are mutually exclusive events, then, P (A or B) = P(A)+ P(B).Or, P(B) = P (A or…

Q: Example 2.3.11 Show that for any two events A and B, P(AN B) s P(A) s P(A U B) s P(A) + P(B) nned…

A:

Q: If E and F are two independent events, and P(ENF)=0.56, P(E)=r, and P(F)=y, then which one is the…

A:

Q: Suppose X and Y are jointly continuous random variables, the conditional expectation of u(x), given…

A: The conditional expectation of u(x) given y is:

Q: 1. Suppose that E and F are independent events such that Pr[E] = .3 and Pr[F] = .4. (f) Calculate…

A: P(E) = 0.3 P(F) = 0.4

Q: Suppose that X and Y are random variables with E(XY) = E(X)E(Y). Then X and Y * independent. Also…

A: We know that if X and Y are independent then E(XY)=E(X)E(Y). But the converse is not always true.…

Q: If A and B are two independent events such that P(AUB) = 0.8, and P(A) 0.3, %3D then Find P(B)?

A:

Q: If A and B are independent events such that P(A) = 0.4 and P %3D

A: Concept: If the probability of occurrence of one event is not affected by the probability of…

Q: Theorem 3.16. For any three events A, B and C, Р (AnB IC)+ P (AnBIC)- Р (AI C)

A:

Q: Q1: If the event A is independent with itself, then P(A) is

A: The statement is the event A is independent itself.

Q: A and B are independent events. If Pr(A intersect B)= 0.32 and Pr[A]= 0.4 what is Pr [B]?

A: Given Data: The probability of A intersect B is: PrA∩B=0.32 The probability of A is: PrA=0.4 Event A…

Q: According to Jane, two particular events happened at the same time. T/F: According to Penny, these…

A: 3. To check whether the information is true or not.

Q: Siven that P(A) = 0.06, P(B) = 0.23, and P(A and B) = 0.0258, are events A and B ndependent? %3D %3D…

A:

Q: 6- If the event A is included in the event B than: a) P(AsB) b) P(A2B) c) P(1-P(A)) d) P(1-P(B)) 7-…

A: Solution

Q: Let X1 ~ x² (n, 8) and X2 ~ x² (m, 2) : mX1 find the expected value of X = nX2 Е (X).

A: We have given two chi square distribution and we have to find the mean of  resultant F distribution.

Q: Suppose the p.d.f. of random variable X is defined as x³/20 if1<x< 3 f(x) = otherwise

A:

Q: Suppose that we have two events, A and B, with P(A)=0.60,P(B)=0.70, and P(A∩B)=0.40 a. Find P(A∣B)…

A:

Q: Compute the probability of each of the following events (i) X <1 1/2 (ii) XY is even

A:

Q: Let A  and B be two events such that P (A) = 0.46 and P (B) = 0.07 (a) Determine P (A ∪ B), given…

A: Given: A and B be two events such that P (A) = 0.46   P (B) = 0.07

Q: If x is functionally related to A and B as x = A + B, and if A and B are random variables, then x is…

A:

Q: 3 b. X and Y are two events, P(Y)==, P(X|Y)=, and PYoX 10 %3D %3D Find P(XnY) and P(X).

A: Given P(Y) = 35, P(X/Y) = 23     and   PY ∩ X = 310

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: A doctor is called to see a sick child. In the neighborhood is known that: 80% of sick children have…

A: Given Information: PF=0.80 PM=0.20 PR | M=0.95 PR | F=0.08

Q: where P = 0 when an event (never occurs) and P = 1 when the event is. Оа. sure (always occurs) b.…

A: Given problem Given that   P = 0 when an event never occurs  P = 1 when the event is sure ( always…

Q: Let Y1 and Y2 be independent random variables with Y; ~ N (0, 1). 1 Let 1-[":]+c[ %] where C:2 x 2 =…

A: From the given information, Y1 and Y2 are independent random variables with Yi~N0, 1. That is,…

Q: 1. These are the events that cannot happen at the same time. a. mutually exclusive b. non mutually…

A:

Q: Suppose that for three dice of the standard type all 216 outcomes of a throw are equally likely.…

A:

Q: (4) Let X be a random variable with p.d.f. 2e-2x 0<x<0 f(x)= , find E(e2x) O.w

A: Random Variable: A random variable is a real valued function that assign a real number to each…

Q: Suppose (X,Y) is a continuous random variables with joint probability d 4xy Osxs1,0sys1 x,Mx.v) = {"…

A: Let X be a random continuous variable with probability density function(pdf) f(x) then the expected…

Q: Theorem 3-14. For a fixed B with P( B) > 0, P (A \ B) is probability function.

A:

Q: Suppose that X and Y are random variables with E(XY) = E(X)E(Y). Then X and Y * independent. Also…

A: E(XY) = E(X)E(Y)

Q: 2. Suppose that a random variable X has a discrete distri- bution with the following p.f.: cx for x…

A:

Q: Suppose that C and D are mutually exclusive events such that P(C) = 0.14 and P(D) = 0.32. Determine…

A: Given, P(C) = 0.14  P(D) = 0.32  P(C or D)=?

Q: If A and B are two independent events where P(A) = 0.2 and P(B) = 0.3 , then P(AN B) = %3D O 0.2 0.5…

A:

Q: J A and B are independent events, prove that the events A and B,A and B; and A and B are also…

A:

Q: Suppose that X₁, X₂, X3 are mutually independent random variables with the respective generating…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: If X is a continuous random variable, argue that P(x, SXS x₂) = P(x₁ < X < x₂) = P(x₁ < X < x₂) =…

A: As per guidelines we are supposed to solve the maximum first questions at  a time.kindly post…

Q: Let A and B be two events such that P(AC) = 0.70, P(B) = 0.50, and P(A U B) = 0.60. What is P(An B)?

A:

Q: Suppose that A, B and C are three independent events such that P(A)=0.2, P(B)=0.5 and P(C)=0.1.…

A:

Q: If E and F are mutually exclusive events with P(E) = 0.11 and P(F) = 0.38, then the value of P(EUF)…

A: Given that P(E) = 0.11, P(F) = 0.38

Q: Consider the following two events for a randomly selected adult: Y = N = this adult has shopped on…

A:

Q: IJ A and B are independent events, prove that the events A and B, A and B; and A and B are also…

A: Answer: For the given data,

Q: For any event A, P (A U Ã) =1 True or false

A: for any event A, A¯  is complement of A. then A¯∩A=∅

Q: 4.Suppose that X is a random variable for which E(X)=µ and Var(X)=o². Show that E(X(X-1)]=µ(µ-1)+o?

A: It is given that E(X) = μ and Var(X) = σ2

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.