6. [Maximum mark: 5] The following table shows the probability distribution of a discrete random variable X, where a, ke R*. X 1 2 3 4 P(X=x) k k² a k³ Given that E(X) = 2.3, find the value of a.

Q: Let X be a random variable with the probability distribution below. Find Horx), where g(X)= (2X+3)-.…

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Q: Let X1, X2, X3 be i.i.d. random variables N(0, 1). Show that Y1 = X1+8X3 and Y2 = X2+8X3 have…

A: Solution:         ut   x1    x2 , x3    iid ~N(u=0, α2=1)         ut  Y1 = x1 +δ x3 & y2= x2+δx3…

Q: Q3. The moment generating function for a random variable X is e3t M(t)=1-t2¹ What are the mean and…

A: The moment generating functionMx(t)=e3t/(1-t2)    -1<t<1To find mean and variance of X Concept…

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: Homework-1: Suppose a continuous random variable X has the following probability density e 2, x >0…

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Q: Q4. The following table shows the probability mass function for the discrete random variable X: k 2…

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Q: 5.17 A firm has been monitoring its total daily telephone usage. The daily use of time conforms to…

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Q: Question 2. Let X be a normal random variable with u = -5 and o² = 4. a) Find P(X –3|X > -5).

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