If X is a random variable with Binomial distribution of n=35 and p=0.45, find: i. E(X) ii. Var(X) ii. P(X<4)

Q: Let X be a random variable with mean E[X] = 20 and variance Var(X)= 3. Define Y = 3 - 6X. Calculate…

A: We have given that, Let X be a random variable with mean E[X] = 20 and variance Var[X] = 3   We know…

Q: The random variable X can only take the values ​​1, 2, 3 and 4 with equal probability. Determine the…

A: Given information: A random variable X has been given that can take only values 1, 2, 3 and 4. The…

Q: Let X be a random variable having the binomial distribution with size n and probability p E (0,1).…

A:

Q: The random variable X has a Poisson distribution with a mean value of 6. According to this P(2 S…

A: Probability=0.268

Q: Q2: What is the expectation and the variance of RV X, where X represents the out come throwing a…

A: Answer:-  Q2)Let X be the number of outcomes after throwing a die.

Q: Since P {x=-1} = P {x=1} = 1/2 , calculate the expected value and variance of the X random variable.…

A: Solution: From the given information,

Q: If a random variable X follows Poisson distribution such that P (X = 1) = P (X = 2) find (a) the…

A:

Q: Q3: let x be random variable with Beta distribution, find the V(x)?

A: Beta Distribution: A continuous random variable X is said to follow Beta distribution with…

Q: Decide whether the random variable x is discrete or continuous. x represents the length of time it…

A: We know that discrete variables take a finite number of countable points whereas a continuous random…

Q: The random variable X has a Poisson distribution such that P(X= 0) = P(X = 1). Calculate P(X= 2).

A:

Q: let X denote a random variable that has a Poisson distribution with mean y = 3 find p(x≥4/x≥2)

A:

Q: 2n- 50 and p= 0.45

A: Given, Let, n =number of trials p =the probability of success q=1-p

Q: 6. Given a random sample X₁, X2, ..., Xn from a normal distribution with known mean μ = 0 and…

A:

Q: The random variable X has a binomial distribution with n = 6 and p = 0.3. Calculate: P (X 2 5)

A: Givenn=6p=0.3x~Binomial(n=6,p=0.3)P(X=x)=(nx)×px×(1-p)n-x ;  x=0,1....,n

Q: Let X and Y be two independent random variables from exponential distribution with mean 3 and 4,…

A: The joint pdf of X and Y can be obtained as f(x, y) = f(x).f(y)

Q: Since x is a Poisson-distributed random variable with a mean of 1.8, what is its standard deviation?…

A: For a Poisson-distributed random variable X, the mean of X is equal to the variance of X.

Q: The random variable X has a binomial distribution with parameters n = 8 and p = 0.30. what is…

A: The formula for binomial distribution is, PX=x=nxpx1-pn-x

Q: For an initial investment of 100, an investment yields returns of Xi  at the end of period i for…

A: Given that, the initial investment is 100 and the investment yield is X1 and X2 at the end of period…

Q: q-1The random variable x is known to be uniformly distributed between 0.5 and 2.5. What is the…

A: It is given that X follows Uniform(a = 0.5 and b = 2.5)

Q: Let X be a random variable that follows the Poisson distribution with a mean of Find: a. Р(X-0) b.…

A:

Q: 2. Show how the Poisson distribution -m m e (x= 0, 1, 2,...) %3D х! can be regarded as the limiting…

A:

Q: Let X1 be a normal random variable with mean 2 and variance 3 and let X2 be a no random variable…

A: Given that X1 follows Normal distribution with E(X1)=2 and V(X1)=3. X2 follows normal distribution…

Q: The random variable X has a Poisson distribution such that P(X=0)=P(X=1).  Calculate P(X= 2).

A:

Q: X is a normal random variable with mean 0 and standard deviation 1. Y is uniformly distributed…

A: We are given the following X~N0,1 &amp; Y~U2X,0fx=12πe-12x2⇒2X&lt;Y&lt;0  or  2Y&lt;X&lt;0

Q: Let X be a binomial random variable with a mean of 0.5 and a variance of 0.45. Find P(x=4).

A: Solution

Q: Let the random variable X fit the binomial distribution with p=1/2 , n=3 parameters. Plot the…

A: Given Data: n=3 p=0.5   Distribution function is also known as cumulative function

Q: Let X₁, X2, X3, X4, X5 be an independent and identically random variables following a Binomial…

A:

Q: Suppose you have a chi-square random variable, Y, with 10 degrees of freedom. What is the smallest…

A: Given: Y~χ102   PY&gt;k&lt;0.05  ................(1)

Q: Let X and Y have a bivaraite gamma distribution of Kibble with parameters a = 1 and 0<0< 1. What is…

A:

Q: If X1 and X2 are independent random variables hav-ing the geometric distribution with the parameter…

A:

Q: If X follows a binomial distribution with p = 0.1 and n =100, find the approximate value of P(2 ≤ X…

A: 1. In normal approximation, μ=np=1000.1=10σ=np1-p=100.9=9=3 And Z=X-npnp1-p Then,…

Q: Suppose random variable X has a Poisson distribution with t​ = 2 and λ= 4. What is​ E(X)?

A:

Q: if Y1 and Y2 are independent Poisson random variable with parameters λ1 and λ2 re- spectively. Then…

A:

Q: Q2: What is the expectation and the variance of RV X, where X represents the out come throwing a…

A: If X is the outcome from the throw of a die then there are 6 possible values of X that are 1, 2, 3,…

Q: Suppose that the random variable Y has a binomial distribution with n trials and success probability…

A:

Q: If the variance of a Poisson variate is 3. Find the probability that, ne (1) x =0 (ii) 1Sx<4 eor…

A: GivenThe variance of a poisson variate is 3in poisson distribution the parameter of mean and…

Q: Consider a random sample from the distribution of Binomial, Poisson, Exponential, Gamma, and normal.…

A: Binomial: Let Xi~Bn,p, the the p.m.f of Xi is given by, px=nCxpxqn-x,x=0,1,2,...,n Then, EXi=np and…

Q: What is Pr(X = n) for a Poisson random variable with parameter l? What is E(X ) in this case?

A: The parameter of the Poisson random variable is l.

Q: If the time taken to repair a personal computer is a random variable X whose p.d. f is given by · ,0…

A:

Q: X has a random variable with Poisson distribution A = 2. Accordingly, what is the probability value…

A:

Q: Find the approximate mean and variance of Y = √X, where X is a random variable following a Poisson…

A:

Q: Q4: Suppose that X has a discrete uniform distribution on the integers 0 through 9. Determine the…

A: According to the given information, we have X follows discrete uniform distribution with parameters…

Q: The random variable X has a binomial distribution with n=6 and p=0.3. Calculate P(X greater than or…

A: Given,n=6p=0.3A random variable X~Binomial(n=6 , p=0.3)P(X=x)=6x 0.3x1-0.36-xP(X=x)=6x 0.3x0.76-x  ;…

Q: If a random variable X has a binomial distribution with parameters n = 15 and p = 0.5, find : P(10…

A: Given, X has a binomial distribution with parameters n=15 and p=0.5 Therefore, the probability mass…

Q: Q4: Suppose that X has a discrete uniform distribution on the integers 0 through 9. Determine the…

A:

Q: Let X be a random variable that follows the Poisson distribution with a mean of 6. Find: a. РX-0) b.…

A:

Q: Suppose that for a stochastic variable X~B(n;p) with the parameters n = 10 and p = 30% a) BY HAND…

A: Given that X follows binomial distribution with parameters n=10 and p=0.3 a) We know that for a…

Q: Let X be a binomial random variable with a mean of 0.5 and a variance of 0.45. Find P(x is greater…

A:

Q: Let X be a discrete random variable with PGF P(s) = a. Find the probability distribution of X. b.…

A: * SOLUTION :-    From the given information the answer is provided as follows