Question

4. Given x: -3 / 0 / 3 P(X =x): .5 / .2 / .3 Find the variance given that the expected value is - .6

A. 4.1 B. 2.85 C. 8.142 D. 2.02 E. 6.84

5. A probability distribution has a mean of 10 and standard deviation of 1.5. Use Chevbychev’s Inequality to estimate the probability that an outcome will be between 7 and 13.

A. 4 B. 2 C. 5 D. 4

Answer #1

You are given the following Discrete Probability Distribution
p(x)
Row
x
P(x)
1
1
0.1
2
2
0.156
3
3
0.147
4
4
0.2
5
5
0.222
6
6
0.056
7
7
0.02
8
8
0.099
1
Provide the following:
Mean (Expected value)
Variance
Standard Deviation
Graph (Histogram) of the Probability Distribution

Consider the following probability distribution table:
X
1
2
3
4
P(X)
.1
.2
.3
.4
If Y = 2+3X, E(Y) is:
A.7 B.8 C.11 D.2
19.
If Y=2+3X, Var (Y) is:
A.9
B.14
C.4
D.6
20.
Which of the following about the binomial distribution is not a
true statement?
A. The probability of success is constant from trial to trial.
B. Each outcome is independent of the other. C. Each outcome is
classified as either success or failure. D....

1. Find P{X = x} for x = 0, 1, 2, 3, 4, 5 for a Bin(5, 3/7)
random variable.
2. Find the first and third quartiles as well as the median for
a Beta(3, 3) random variables.
3. Find P{X ≤ x} for x = 0, 1, 2, 3 for a χ 2 2 random
variable.
4. Simulate 80 Pois(5) random variable. Find the mean and
variance of these simulated values.

The probability distribution of a random variable X is given
below.
x
3
4
6
7
9
P(X = x)
10/29
2/29
6/29
4/29
7/29
Given the following mean
Find the variance (Var(X)) and the standard deviation,
respectively.
a) [5.59, 2.37]
b) [1101.00, 33.18]
c) [1828.91, 42.77]
d) [22.86, 4.78]
e) [44.92, 6.70]

Find the mean, variance and standard deviation for the
probability distribution given below:
X: -5, 2, 12, 8,
P(X): 0.575, 0.142, 0.209, 0.074
A. Mean =
B. Variance =
C. Standard Deviation =

The probability distribution of a random variable X is
given.
x
−4
−2
0
2
4
p(X =
x)
0.2
0.1
0.3
0.2
0.2
Compute the mean, variance, and standard deviation of
X. (Round your answers to two decimal places.)
Find mean, variance, and standard deviation

Find the mean, variance and standard deviation for the
probability distribution given below:
X
0
5
8
10
P(X)
0.598
0.136
0.208
0.058
A. Mean =
B. Variance =
C. Standard Deviation =

Given p(x) = ? 3(?+4) 3 on [0, ∞), Find the constant C such that
p(x) is a probability density function on the given interval and
compute ?(0 ≤ ? ≤ 1).

(4% = 2% for each part)
Given the following discrete probability distribution:
x 5 6 7 8
P(x) 0.35 0.45 0.15 0.05
a) Calculate the expected value of X (E(X) = μX).
b) Calculate the standard deviation of X (σX )

Suppose X is a random variable with p(X = 0) = 4/5, p(X = 1) =
1/10, p(X = 9) = 1/10. Then
(a) Compute Var [X] and E [X].
(b) What is the upper bound on the probability that X is at
least 20 obained by applying Markov’s inequality?
(c) What is the upper bound on the probability that X is at
least 20 obained by applying Chebychev’s inequality?

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