Question

Let X be a discrete random variable with values 1,2,3,4,5 and corresponding proba- bilities 1/7, 1/14, 3/14, 2/7, 2/7. a) Compute E(X) b) compute E[|X − 2|].

Answer #1

**Solution:**

X | P(X) | X.P(X) |

1 | ||

2 | ||

3 | ||

4 | ||

5 | ||

Total | 1 |

a) Compute E(X)

**Answer:**

b) compute E[|X − 2|]

Let X be a discrete random variable that takes on the values −1,
0, and 1. If E (X) = 1/2 and Var(X) = 7/16, what is the probability
mass function of X?

Q6/
Let X be a discrete random variable defined by the
following probability function
x
2
3
7
9
f(x)
0.15
0.25
0.35
0.25
Give P(4≤ X < 8)
ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ
Q7/
Let X be a discrete random variable defined by the following
probability function
x
2
3
7
9
f(x)
0.15
0.25
0.35
0.25
Let F(x) be the CDF of X. Give F(7.5)
ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ
Q8/
Let X be a discrete random variable defined by the following
probability function :
x
2
6...

Let X be a discrete random variable with the range RX = {1, 2,
3, 4}. Let PX(1) = 0.25, PX(2) = 0.125, PX(3) = 0.125.
a) Compute PX(4).
b) Find the CDF of X.
c) Compute the probability that X is greater than 1 but less
than or equal to 3.

The range of a discrete random variable X is {−1, 0, 1}. Let MX
(t) be the moment generating function of X, and let MX(1) = MX(2) =
0.5. Find the third moment of X, E(X^3).

The range of a discrete random variable X is {−1, 0, 1}. Let
MX(t) be the moment generating function of X, and let MX(1) = MX(2)
= 0.5. Find the third moment of X, E(X^3 )

1. Let X be a discrete random variable with the probability mass
function P(x) = kx2 for x = 2, 3, 4, 6.
(a) Find the appropriate value of k.
(b) Find P(3), F(3), P(4.2), and F(4.2).
(c) Sketch the graphs of the pmf P(x) and of the cdf F(x).
(d) Find the mean µ and the variance σ 2 of X. [Note: For a
random variable, by definition its mean is the same as its
expectation, µ = E(X).]

Let X be a discrete random variable with probability mass
function (pmf) P (X = k) = C *ln(k) for k = e; e^2 ; e^3 ; e^4 ,
and C > 0 is a constant.
(a) Find C.
(b) Find E(ln X).
(c) Find Var(ln X).

Let the random variable X have a discrete uniform distribution
on the integers 1 ≤ x ≤ 7. Determine the mean, μ, and variance, σ2,
of X. Round your answers to two decimal places (e.g. 98.76). μ = σ2
=

Let X be a random variable with possible values {−2, 0, 2} and
such that P(X = 0) = 0.2. Compute E(X^2 ).

Let x be a discrete random variable with the following
probability distribution
x: -1 , 0 , 1, 2
P(x) 0.3 , 0.2 , 0.15 , 0.35
Find the mean and the standard deviation of x

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 17 minutes ago

asked 17 minutes ago

asked 22 minutes ago

asked 23 minutes ago

asked 26 minutes ago

asked 33 minutes ago

asked 37 minutes ago

asked 42 minutes ago

asked 42 minutes ago

asked 44 minutes ago

asked 50 minutes ago

asked 51 minutes ago