A and B are independent events. If Pr[A]=0.3 and Pr[B]=0.7, what is Pr[A∩B′]?

Q: E and F are mutually exclusive events. P(E) = 0.3; P(F) = 0.2. Find P(E | F) %3D

A: Given that E and F are mutually exclusive. P(E)=0.3 and P(F)=0.2

Q: A random variable X is defined by X =- 2 = 3 with a prob. of 113 with a prob. of 1/2 with a prob. of…

A: Given, X -2 3 1 P(X) 1/3 1/2 1/6

Q: E and F are events such that Pr[E] Pr[F|E] Pr[F|E] = 0.6 = 0.1 0.9 %3D Find Pr[F]. (A) 0.36 (B) 0.06…

A:

Q: If a random variable X is defined such that: E[(X- 3)2] = 18 and E[(X- 1)²] = 34. Then the values of…

A:

Q: (1) Let X be a random variable with p.d.f. -8x 0<x<0 k f(x)=. , find k. O.w

A: Step 1: Given,                            f(x) =1k e-8x0, 0&lt;x&lt;∞ We know that ,…

Q: If a probability generating function of a random variable x is Px(s)=(1/3+2/3s)^6 determine…

A: Given: The probability generating function of a random variable X is given as:…

Q: If a random variable X is defined such that: E[(X – 2)²] = 18 and E[(X+1)²] = 33. Then the values of…

A: Given: E( (X - 2 ) 2 )= 18 E( (X + 1 ) 2 )= 33

Q: If a random variable X is defined such that: E[(X- 3)2]= 18 and E[(X- 1)] = 34. Then the values of u…

A: Given that; E[(X-3)2]=18 and;E[(X-1)2]=34 We need to find the values of μ and σ.We know…

Q: Q.2 Find the probability generating function of :1) P(X=2n) 2) P(X<n).

A: If X and Y are non-negative independent integral valued discrete random variables with respective…

Q: Prove that for a continuous random variable X,E (aX+ b) = aE (X) + b.

A:

Q: If a random variable X is defined such that: E (X + 4) = 10 and E[(X + 4)²] = 112. Then the values…

A: The image is attached below,

Q: 21. Let the random variable X have the moment generating function e3t M (t) -1 <t < 1. 1- t2 ' What…

A:

Q: The PMF of the number N of customers that arrive at a local li- brary within a one-hour interval is…

A: Solution

Q: B. Let X and Y be random variables and let A e B. Prove that the function

A: SOLUTION ;

Q: Q1. Suppose that X and Y are jointly continuous random variable (у — х for 0<x < 1 and 1 < y < 2 - x…

A: We have given joint pdf of X and Y we have to find answers of related questions.at bartleby we…

Q: Suppose X1 has the binomial distribution b(4, 0.5), X2 has the binomial distribution b(6, 0.75), and…

A:

Q: If the joint probability distribution of X1 and X2 isgiven by f(x1, x2) = x1x236for x1 = 1, 2, 3 and…

A:

Q: • For random variables X and Y and scalar constants a and b, we have E[aX + bY] = aE[X] + bE[Y], ||…

A:

Q: E and F are mutually exclusive events. P(E) = 0.1; P(F) = 0.6. Find P(E | F) %3!

A:

Q: 1. The probability that the interval (x-0/4, + o/4) contains u is equivalent to P(

A: 1. The probability that the interval contains μ is x¯-σ4, x¯+σ4.

Q: If a random variable X is defined such that: E[(X – 3)²] = 18 and E[(X – 1)²] = 34. Then the values…

A:

Q: If the p. d. f of a random variable X is f(x) = 1,0 ≤ x ≤ 2, then P(X> 1.5|X > 1) is

A:

Q: 3.a. Fill in the blank and prove the resulting statement: If X is a random variable and t is a…

A: Result E(ax+b)=aE(x)+b  V(ax+b)=a^2V(x) Given  E(x)=7 , V(x)=2

Q: If Mx (V) is a moment generating function of a random variable X, then M(cv) = Mcx (v), wherec is a…

A:

Q: Q3.The relay network in figüre, operates if and only if there is a closed path of relays from left…

A: Given: The network operates only if there is a closed path of relays from left to right. Consider…

Q: For a 1.0 x10-26 g particle in a box whose ends are at x = 0 and x = 2.000 Å, calculate the…

A:

Q: (a) Show that for any non-negative random variable X, we have E(X)= P(X > t)dt (b) Let the CDF of X…

A: For a continuous random variable X, the probability density function(PDF) is denoted by fXx and it…

Q: Let X1 and X2 be two independent random variables. X1 is normal N(1,4) and X2 is normal N(1,2).…

A:

Q: If øx(@) is a characteristic function of a random variable X, then , (co) = 6, (@), where c is a…

A:

Q: Let X be the discrete random variable with the probability function f (x) = kx³ + 0.15 %3D for x =…

A:

Q: There is a random variable X such that E(x)= 4, and E (x²)= 23 Select one: O True O False

A: Given: E [X] = 4 E [ X2] = 23

Q: If a random variable X is defined such that: E[(X – 2)²] = 18 and E[(X+1)²] = 33. Then the values of…

A: The given equations are EX-22=18 and EX+12=33. Now,…

Q: If a random variable X is defined such that: E[(X – 2)²] = 18 and E[(X+1)²] = 33. Then the values of…

A:

Q: If a random variable X is defined such that: E[(X – 2)*] = 18 and E[(X +1)*] = 33. Then the values…

A:

Q: E and F are mutually exclusive events. P(E) = 0.3; P(F) = 0.2. Find P(E | F) %3D %3D

A: It is given that the events E and F are mutually exclusive.

Q: 2. Let X be a discrete random variable whose range is the nonnegative integers. Show that E[X]=…

A: # discrete random variable x with non negative integers  Then to prove that E(x)=sum(1-F(x))  F(x)…

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: 5. Calculate the value of k so that the function f(x) = k/5ª. N, set a probability function of a…

A:

Q: (1) Let X be a random variable with p.d.f. -8x 0<x<0 k f(x)=< , find k. O.w

A: Given information: It was stated that X is a random variable. The probability distribution…

Q: If a random variable X is defined such that: E[(X - 3)2] = 18 and E[(X+1)²] = 34. Then the values of…

A: Variance(X)=E[(x-mu)2].

Q: - Show that P(w) = ,w = 0,1,2,..,1 >0 1+11+1 qualifies as a discrete probability function. 3

A: Condition for discrete probability distribution All probabilities are greater than 0 sum of…

Q: Consider a random variable X taking the values k1, k2, ·.. , kn E R with probability P1, P2, ; Pn E…

A: Formula is

Q: If a random variable X is defined such that: E[(X - 2)²] = 18 and E[(X+ 1)'] = 33. Then the values…

A:

Q: Q1: Let X1, X2~iid U(0,1), find the probability that the random interval 3X2' X2 includes . 3

A:

Q: Let X be a random variable taking positive values and assume that E(X) exists. Which of the…

A: Option (I) is correct as E(X2)&gt;= (E(X))2 when we find Variance.

Q: 12y 3p A) For the joint probability p(A.B)-5p 4y. Find P(A). P(B), P(A/B), and 13p 7pl P(B/A), if y…

A:

Q: Suppose that 30% of all people who buy a new Iphone also buy an Apple watch. Consider randomly…

A: Let X represent the number of those who also bought an Apple watch. Here X follows Binomial…

Q: E and F are mutually exclusive events. P(E) = 0.1; P(F) = 0.6. Find P(E | F) %3D

A: Given: P(E)=0.1P(F)=0.6

Q: (a) Find E(X). 1 DUY Suppose X is a random variable with cdf 0 F(x)= x(2-x) 1 for x 1

A: Given: X is a random variable with CDF,  F(x)= x(2 - x)  ;0&lt;x&lt;1

Q: 6. Imagine that a zealous prosecutor (P) has accused a defendant (D) of com- mitting a crime.…

A: *Answer:  *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.