Let X be a random variable with probability distribution as shown below: -l

Q: (a) Find the expectation E (X) of X. E (x) = [ (b) Find the variance Var(X) of X. Var (x) = 0

A: Consider , the table , x P(x) x*P(x) x^2*P(x) 0 0.4 0 0 1 0.05 0.05 0.05 2 0.15 0.3 0.6 3…

Q: The probability distribution function of the discrete random variable X is x -1 0 2 5 P(X=x) 0.10…

A: Given :   X -1 0 2 5 P (x) 0.10 0.50 0.30 0.10

Q: Let X be a random variable with cumulative distribution function F(x) = 1-e" for a> 0. What is P(0 <…

A: Correct answer is   0.75

Q: F(x) = x < -1 = 0 F(x) = -1 ≤ x < 0 = .15 F(x) = 0 ≤ x < 2 = .3 F(x) = 2 ≤ x < 3 = .5 F(x) = 3 ≤…

A: Solution

Q: Let X be a random variable such that E(X) = 3 and E(X') = 13. Use Chebychev's inequality to…

A:

Q: (a) Find the expectation E (X) of X. E (x) = | %3D (b) Find the variance Var(X) of X.

A: The E(X) is defined as E(X) = ∑x.P(X = x) And variance of X is  V(X) = E(X2) - (E(X))2

Q: a) Find the expectation E (X) of X. E (x) = | %3D (b) Find the variance Var(X) of X. Var (x) = 0

A: Here given discrete probability distribution of x  Here use expected value and Variance formula

Q: b) Let X be the random variable with the cumulative probability distribution: 0, x < 0 W F(x) = kx²,…

A:

Q: 1. Let X be a Poisson random variable with parameter A. Derive E(X) and E(2x)

A:

Q: Let X be a random variable with p.d.f. 0<x<0 S(x) = • ,find E(e3) O.w

A: Hey there! Thank you for posting the question. Since there are multiple questions posted, we will…

Q: b) Let Y, and Y, be discrete random variables with a joint probability distribution as shown in the…

A: Given: The joint probability distribution of the random variable Y1 and Y2 is provided as:…

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

A:

Q: If the joint cumulative distribution function of random variables X and Y is F(x,y) = (1 – e*)(1 –…

A: The joint cumulative distribution of X and Y is given by, F(x,y) = (1-e-x) (1-e-y)   x&gt;0,y&gt;0…

Q: Let the probability function of the random variable X be defined as f(x)=cx(1-x) for 0<x<1,…

A: f(x) = c(x-x2)   a)We know that, ∫abf(x)dx = 1 ∫01c(x-x2)dx = 1 c(x22-x33)]01 = 1 c(12-13) = 1 c = 6…

Q: The probability distribution function of a discrete random variable X is x2 55 ,x = 1,2,3,4,5 0,…

A: Find  Var(3X+2)=? 5E(2X-1)=? E(2X+1)2=?

Q: For a continuous random variable X. we can compute the probability of P (a < X<b) by O Fibl-Fla) O…

A: GivenP(a&lt;X≤b)

Q: The probability of an event depends on the random variable X and can be expressed by the following…

A: Given:P(A|x)=1-e-kx ;x≥0 where k&gt;0Given that X is a normally distributed random variable with…

Q: Let x be an exponentially distributed continuous random variable, with f(x) = ce¯«, for 0 < x < «,…

A: a) Consider,…

Q: A discrete random variable X has the probability distribution as follows: *(x)= 5-x ;x%- 1,2,3,4 10…

A:

Q: Let X₁ and X₂ be independent exponential random variables, with parameters X₁ and 2, respectively.…

A: Given : X1 and X2 are two independent exponential random variables with parameter lambda1 and…

Q: 1. For any random variable X for which E(X) and E(X²) are finite, show that Var(X) = E(X²) – [E(X)]²…

A:

Q: If X and Y have the joint probability distributionf(−1, 0) = 0, f(−1, 1) = 1 4 , f(0, 0) = 16 , f(0,…

A: The joint probability distribution of the random variables is given as follows:

Q: For the discrete random variable X, P(X = 1) = p = 1 – P(X = -1). Please find c so as to be E(cX) =…

A:

Q: . The cumulative distribution function of a discrete random variable X is x< 0 1 0 <x<1 3 7 F(x) = |…

A: From the given information, Fx=0       x&lt;013    0≤x&lt;1712    1≤x&lt;21724    2≤x&lt;31…

Q: Let X1 ~ N (0, 1), X2 ~ N(0,1), and X3 ~ x(n) be mutally independent random variables. Find the…

A: Given information X1, X2 follows normal and X3 follows the chi-square distribution General condition…

Q: The cumulative distribution function F(x) for a random variable X is given as: for x 4 Find P(1 < X…

A:

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

A:

Q: Let X be a continuous random variable with cumulative distribution function X < 0 x3 0 < x < 3 27…

A: Given,   P(X&gt;3)=?

Q: Let X be a continuous random variable with probability distribution as shown below: (x*(2x +), if0 <…

A:

Q: The continuous random variable X has a cumulative distribution function F(x) given by: x 2. Find…

A: The probability distribution function is the derivative of the cumulative distribution function.

Q: 0, x)

A: a) The required value is calculated as follows: fx=ddxFx      =ddxx24     =2x4     =x2…

Q: Let X and Y be two independent exponential random variables. X ~

A: Given,  X and Y be two independent exponential random variables.                       X~exp(1) and…

Q: The distribution function of the random variable X isgiven byF(x) = 1 − (1 + x)e−x for x &gt; 00 for…

A: The required probabilities are as follows:

Q: Let X be a random variable such that E[X] = 0 and P(-3 < X < 2) = 1/2. Find a non-trivial lower…

A: Given information: The expectation of the random variable X is E(X) = 0 and P(-3 &lt; X &lt; 2) =…

Q: Let X be a discrete random variable with probability function f(x) = kx for x = 1,2,3,4. The value…

A:

Q: Let X be the random variable with the cumulative probability distribution: 0 x < 0 F(x) = {₁ - e-²x;…

A:

Q: a) Find the expectation E (X) of X. E(X) = 0 (b) Find the variance VarX) of X. Var(X) = 0

A: Given: x P(x) 0 0.35 10 0.35 20 0.05 30 0.25 Total 1

Q: Denote by { 1* 0 <x<1 0.5 2< x <c . elsewhere f(x) = Find the value of c, such that f(x) is the…

A: Solution: From the given information,

Q: Define the random variable X as the proportion of voters in a certain county that approve of a ew…

A:

Q: The probability mass function of a discrete random variable X is given as: (x² +5x) x = 1,2 f(x)%3=…

A: Solution: From the given information, the probability mass function of X is

Q: Let X be the random variable with the cumulative probability distribution: 0 x < 0 F(x) = {₁ - e -²x…

A:

Q: Let X be a random variable with p.d.f. 2e-2x 0< x<00 f(x) = , find E(x). O.w

A: We know that, E(x)= integration |x X*f(x) dx

Q: If g,(x) and g,(x) are two functions of a random variable X, then E[g (x)+ g,(x)] = E[g,(x)]+…

A:

Q: The distribution function of a random variable X is given by 0, for x 1. Find (a) P(-< X < }); (b)…

A: From the given information, Distribution function can be expressed as: Now PDF can be drawn from…

Q: a) Find the value of the constant c

A: The joint pdf is given by f(x,y) = c(2x+y)

Q: Let discrete random variables X and Y have the following probability distribution: Y 1 2 -1 0.10…

A: Expectation of Joint Distribution: Let X and Y be two jointly distributed discrete random variables…

Q: Given that f(x, y) = (2x+2y)/2k if x = 0,1 and y = 1,4, is a joint probability distribution function…

A: Solution: The joint probability distribution function for the random variables X and Y  can be…

Q: X is a discrete random variable with the probability distribution function: k Pr[X = k] 6 -3 10 2 -2…

A: mean=E(X)=∑1nxP(X=x)

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.