A 13 Suppose that P(X = a) = p. P(X = b} = 1- p, a. Show that X-b b. Find Var(X) is a Bernoulli random variable R.D.R EGALA STAT 203 March 4, 2021 A 14 The distribution function of the continuous random variable X is 0, F(x) =31-k a) Find the value of k b) Sketch the graph of F(x) c) Find i. P(X < 4) ii. P(4 6) d) Find the p.d.fof X A 15 A continuous random variable X has the p.d.f. 10- e-a x 20 f(x) 0, x <0 Where c is a constant. a) Find the value of c b) Find the cumu lative distribution function of X and sketch its graph c) Find i) P(X > 8|X > 3) ii) P(X > 1|X < 4)

Q: Q-2: Let X1, X2, ..., X, be independent, exponentially distributed random variables with mean ). 1.…

A:

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

A:

Q: Q1: Let x1, X2. .., Xn, Xn+1 be a random sample of size n + 1,n > 1, from a distribution that is…

A:

Q: 3. Fix a > 0. Let X₁, X₂,... be a sequence of iid random variables with pdf 0-1->1 f(x) = { 02-1 a)…

A: To show that  where $Y$ has the given cumulative distribution function (cdf) FY(y), we will use the…

Q: Which of the random variable is discrete and which is continuous or not? none Continuous Discrete of…

A: Readings of speed counter in the car is continuous variable.

Q: A random variable X has the following PMF: [refer to image] a) Find E(X) b) If Y = g(X) = X^2,…

A: The solution to the problem you provided involves several key concepts from probability…

Q: Let x be a discrete random variable with p.d.f f(x)=ec O* x=1,2,3,.. Oe(0,1), then O=..

A: A random variable can be discrete or continuous. A discrete random variable takes the distinct…

Q: Let Y be a continuous random variable where 1 ,-3< y< 15 f(y) = {18 0 ,otherwise Then expected value…

A: Let  y be a contineous random variable wherefy=118,-3≤y≤150,     otherwise

Q: Question 10. Let X and Y be independent Poisson random variables, each with mean 1. Let T=minimum(X,…

A: In calculating the given probability, we will use the fact that if the minimum of two numbers is…

Q: Question 4. Let X and Y be independent Poisson random variables, each with mean 3. Let T =…

A: As per given by the question,  The mean value is given 3. From Poisson distribution, PX=x=λxe-λx!…

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: 3. Let Y₁,...,Y be a random sample of size 5 from a normal population with mean 0 and v n 15 ΣY. Let…

A:

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: For a uniform random variable U U(16, 29), find the probability P(U <20): P(U <20) D I (Round the…

A: U~U(16,29)a=16 ,b=29

Q: X₁ X₂ X3, and X₁ are normally distributed random variables X₂ The variable(s) which follow(s) a…

A: Determining which variable(s) follow a standard normal distribution:A standard normal distribution…

Q: Q2) Generate 3 Gamma probability distributions of continuous random variable Z with (a = 1ẞ= 1), (a…

A: The Gamma distribution is a continuous probability distribution commonly used in various fields such…

Q: Random variables X and Y have the means and standard deviations as given in the table to the right…

A:

Q: rec 3 Two random variables, X and Y, have independent Poisson distributions given by X- Po(1.4) and…

A:

Q: d has the F(x)= I 0 for x < 1 1 انيا OM N 3 1 2 5 6 for 1 ≤x<4 for 4x6 for 6x10 1 for x 10 P(2<X…

A: X has a distribution function

Q: Let X be a discrete random variable with PMF Px(x)=ca²ª, x=1,2,... where 0 < a < 1. (a) Write down…

A:

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: 10 03 Suppose x is a normally distributed for continuous random variable with A- and - 6. Find value…

A: The provided information is  µ=10 σ=6…

Q: Let X₁, X₂ be 2 mutually independent discrete random variables. The first variable X₁ can be a whole…

A: and  are two mutually independent discrete random variables. is a whole number from to The…

Q: Let x1, x2.X, be a random sample of size (n) taken from N(H1 H2), H2 >0, then alnL(x;2)

A:

Q: Q1: Let x1, X2,.. ,Xn,Xn+1 be a random sample of size n + 1,n > 1, from a distribution tha N(H, o?).…

A: Given Xi~ N(μ, σ2) ; i=1,2,...,n,(n+1)

Q: X1, X2, , nare n independent zero mean Gaussian random variables M] / nis with equal variance o².…

A:

Q: Let P(x) = , x = 0, 1, 2,3 be a probability distribution for a discrete random variable X, find: a)…

A: As per our guidelines we are suppose to answer three sub parts

Q: Let Z be a discrete random variable taking one of the four distributions, Bernoulli, Binomial ,…

A:

Q: b. Suppose of = 2, o% = 2.5, and m = n. Find the sample size n so that X - Ý will be within one unit…

A: X1,X2,...,Xm and Y1,Y2,...,Yn are two samples with  Xi~ N(µ1 ,σ1)  , Yi~ N(µ2 , σ2)  All the random…

Q: 1. Suppose that X is a binomial random variable with n= 200 and p = 0.4. Find the probability PCX<…

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

Q: If X,XXy and Y, Y Y spectively, then the distribution of 2X-F is: are two random samples that…

A: Given that Xi~N0,4 and Yi~N0,25 n1=25, n2=16

Q: i. Show that f(x, a, ß) is a distribution ii. Find E(X)

A:

Q: Student ID: 11) Joint distribution function for two random variables Y 1 and Y2 is given as the…

A:

Q: 5. Consider a strategic bargaining game between two players with a dis- count factor of .75. Find…

A: The barging game model is given by: i2=12,b&lt;12b,b&gt;12 When T=6 xi=T-δ=6=0.75=5.25 Since xi is…

Q: fx(x) 4 a -1a

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

Q: Exercise 4 Suppose X and Y are independent random variables such that X has uniform (0, 1)…

A:

Q: Consider a simple random sample Y1,Y2,...,Yn with pdf f(x,8) - @е ву ө>0, у> 0, then by…

A:

Q: Let X and Y be binomial random variables with distributions of Bi(n, p) and Bi(m, p) respectively.…

A: It is given that the probability generating function of X is, The probability generating function…

Q: respectively. Let f =A prove that 1. f has F distribution with r, and r, degrees of freedom 2. E(f)…

A:

Q: The random variable A has range (0, 1), and p.d.I. given by f(x)=3(x-1)², 0<x< 1. (a) Explain why…

A: Solution: The probability density function of random variable X is  f(x)=3(x-1)2        for…

Q: A5 Let n N and p = (0, 1) with np > 5 and n(1-p) > 5. Which of the following normal distributions…

A: When both np and n(1-p) are greater than or equal to 5

Q: The cumulative distribution function of random vartable X is x 1. Fx (x) = 1 Find: P(Xs1)And P(X=1)

A: P(X≤1)=FX(1)=1 [from the last row of the function]

Q: 2. Suppose a random variable X has the following distribution: 2 10 f(x) 0.2 0.2 0.5 0.1 a) Compute…

A:

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.