Question

Problem 3. Let x be a discrete random variable with the probability distribution given in the following table:

x = 50 100 150 200 250 300 350

p(x) = 0.05 0.10 0.25 0.15 0.15 0.20 0.10

(i) Find µ, σ 2 , and σ.

(ii) Construct a probability histogram for p(x).

(iii) What is the probability that x will fall in the interval [µ − σ, µ + σ]?

Answer #1

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)
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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 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

Let X be a random variable with the following probability
distribution: Value x of X P=Xx 1 0.15 2 0.55 3 0.05 4 0.15 5 0.10
Find the expectation EX and variance Var X of X .

1. Find the missing value indicated by (A) to make this a valid
discrete probability distribution.
x
-10
30
50
90
100
P(X=x)
0.05
0.10
0.25
0.15
A
2. Calculate the mean of the random variable associated with the
following discrete probability distribution. Do not round your
answer.
x
-1
0
1
P(X=x)
0.5
0.2
0.3

Consider the following random discrete distribution.
x
x(P)
24
0.25
30
0.15
49
0.30
58
0.10
60
0.20
Calculate the mean or the expected value of X
Calculate the variance and the standard deviation of the random
variable

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).]

Hello please Use the following discrete probability distribution
below to answer the following questions:
X p(x)
1 0.16
2 0.17
3 0.33
4 0.16
5 0.10
6 UNKNOWN
1. a What is the probability that x = 6?
P(6) = 0.08 P(6) =
0.18 P(6) =
0.24 P(6) = 0.35
1.b) What is the mean of the probability
distribution?
µ =
2.92
µ =
3.11
µ =
3.51
µ = 4.00
1.c) What is the
standard...

Compute the mean and standard deviation of the random variable
with the given discrete probability distribution.
x
Px
−3
0.23
−2
0.15
7
0.25
9
0.27
10
0.1

Problem 1. Let x be a random variable which approximately
follows a normal distribution with mean µ = 1000 and σ = 200. Use
the z-table, calculator, or computer software to find the
following: Part A. Find P(x > 1500). Part B. Find P(x < 900).
Part C. Find P(900 < x < 1500).

A random variable X has the following discrete probability
distribution.
x
12
19
22
24
27
32
p(x)
0.13
0.25
0.18
0.17
0.11
0.16
Calculate σ = standard deviation of X (up to 2 decimal places).

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