Question

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.

Answer #1

a) It is known that

b) The cumulative density function of X is

c) The probability that X is greater than 1 but less than or equal to 3

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...

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).]

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 )

The following table lists the probability distribution of a
discrete random variable x:
x = 0,1,2,3,4,5,6,7
P(x) = 0.04, 0.11, 0.18, 0.22, 0.12, 0.21, 0.09, 0.03
a. The probability that x is less then 5:
b. The probability that x is greater then 3:
c. The probability that x is less than or equal ti 5:
d. The probability that x is greater than or equal to 4:
e. The probability that x assumes a value from 2 to 5:...

X in a discrete uniform(2,4) random variable and given X, W is a
discrete uniform (-x , x) random variable. Find PX,W(x,
w) and calculate it at x=2.
A. 1/27
B. 1/9
C. 1/21
D. 1/15

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

3. Let X be a continuous random variable with PDF
fX(x) = c / x^1/2, 0 < x < 1.
(a) Find the value of c such that fX(x) is indeed a PDF. Is this
PDF bounded?
(b) Determine and sketch the graph of the CDF of X.
(c) Compute each of the following:
(i) P(X > 0.5).
(ii) P(X = 0).
(ii) The median of X.
(ii) The mean of X.

Let
the random variable X have pdf
f(x) = x^2/18; -3 < x < 3 and zero otherwise.
a) Find the pdf of Y= X^2
b) Find the CDF of Y= X^2
c) Find P(Y<1.9)

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|].

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