4. A continuous random variable has the probability density function f(x)=2e-²x X>0 0 x≤0 Find (1) E(X), (ii) E(X), (iii) Var (X), and (iv) SD of X.

Q: 2. Identify the probability density function, then find the mean and variance without integrating.…

A:

Q: 3. If X and Y are jointly continuous random variables with joint PDF fx.y(, y)…

A:

Q: Is f(x) a legitimate probability mass function? (1 – p)"='p =p+ (1 – p)p + (1 – p)²p+ • …· ² 1 x=1

A: We know that to be a legitimate mass function we must have 0≤f(x)≤1 for all x.  And the sum of all…

Q: 7. A random variable has a probability density function given by 1/2 0 ≤ x ≤ 1, 1 ≤ x ≤ 2,…

A: Given the probability density function of the random variable X as

Q: 5) Given X with the probability density function: 4x, if 0<x< 1 0, otherwise fx(x) 6) = Determine…

A: Check the solution in the explanation.Explanation:Check the image below for a detailed solution.

Q: 6) The probability density function of the random variable X whose moment generating function () (1…

A: The moment generating function of X is given by MX(t) = (1/2)(1 + et)

Q: 2- Let the probability density function of the random variable X is - {²()* Then My(t) is (a)…

A:

Q: Q6. (a) The continuous random variable X has a probability density function given by 2 1 C 2 1< x<2…

A:

Q: Two random variables X and Y have a joint cumulative distribution function given by FXY(x, y) = 1/2…

A: Define two cummulative distributions functions such that: F1(x) = 12u(x-2) + u(x-3)=0if x&lt;212if…

Q: 11. The marginal density functions for independent random variables X and Y are g(x) and h(y). Find…

A:

Q: If X is a continuous variable in the range 3 > X > 0 and its distribution function is as follows: F…

A:

Q: (f) The random variable X has the following probability density function: (3x + 3)(x+3)/16 for 00.75…

A: Find  P(X&gt;0.75|X&gt;0.5)=? Cov(X+3,(X+3)-1)=?

Q: A random Variable X has a probability Density function. [(π/16) cos(π x/8) 4 ≤ x ≤4 elsewhere fx(x)…

A:

Q: nd the probability density of the sum W = X + Y.

A:

Q: A continuous random variable X has a probability density function given by dF = ka?e-dx,0 <x < 0o.…

A:

Q: 2. Let X be a continuous random variable with cumulative distribution function P(x) = { ₁-0 + -6x e…

A: The CDF of random variable X is given as: F(x)=1-e-6x    ; x&gt;00                 otherwsie…

Q: 6. If X is a continuous random variable whose probability density function is given by…

A: Given that The probability density function is given by fx=k4x-2x2    , 0&lt;x&lt;20…

Q: 1 (a) ƒ (kx) = 2x+1_2²²₂ = - 2*, x = 1, 2, ..., N, and zero elsewhere (b) f(x)=p(1-p)*, x=0,1, 2,…

A: As per bartleby guidelines we can solve only first three subparts and rest can be reposted  # To…

Q: 3. Let X be a continuous random variable. Let f(x) = c(x − 1)³ and Sx = [1,3]. Hint: (x - 1)³ = x³ +…

A:

Q: 0 a} and (ii) P {X > b} = 0.05

A:

Q: ow that if U and degrees of freedom respectively, then are independent random variables having chỉ-…

A: Hi and thanks for your question! Unfortunately we cannot answer this particular question due to its…

Q: 2. The time taken (in hours) by a response team to attend to a complaint is a continuous random…

A:

Q: 3.For the continuous random variable X with probability density function defined by ¤(2 – x) 0 <x <…

A:

Q: 3. If a random variable has the probability density for x>0 2e-2* f(x) = for x <0 Find the…

A:

Q: The random variable X has probability density function f where f(x)=\ ( kx(x + 1) (2-x ), 0 <= chi…

A: The probability density function is given as,

Q: Let X and Y be two continuous random variables with joint probability density function: 8 xy ;0<…

A:

Q: 5. Suppose that X is a discrete random variable with probability density function p(x) = cx³, (a)…

A: Given, P (x) = cx2        ,   x = 1, 2, 3, 4         = 0          .  Otherwise     To find, a) Find…

Q: Find the probability density of the sum W = X+ Y.

A:

Q: b) Suppose that X is a random variable with the probability density function given by (2(1-x),0 ≤ x…

A:

Q: 5 Suppose the distribution function of the continuous random variable is [1-e*, x>0; F(x)= (0, x3);…

A: (1) The probability that the value of random variable exceeds three, is calculated as,…

Q: Determine P(X < 2)

A: We have to find probability that X is less than 2 for the given probability density function of X.

Q: 4. Let x be a continuous random variable with the following probability density function 3 f (x) =…

A: we have given that  probability density function . and x is a continuous random variable.