Question

- 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

Answer #1

Solution:

Mean = ∑XP(X)

Variance = ∑ P(X)(X - mean)^2

Standard deviation = Sqrt[∑ P(X)(X - mean)^2]

The calculation table is given as below:

X |
P(X) |
XP(X) |
P(X)(X - mean)^2 |

24 |
0.25 |
6 |
90.25 |

30 |
0.15 |
4.5 |
25.35 |

49 |
0.3 |
14.7 |
10.8 |

58 |
0.1 |
5.8 |
22.5 |

60 |
0.2 |
12 |
57.8 |

Total |
1 |
43 |
206.7 |

Part a

Mean = 43

Part b

Variance = 206.7

Standard deviation = Sqrt(206.7) = 14.37706507

Standard deviation = 14.37706507

Consider a random variable X with the following probability
distribution:
P(X=0) = 0.08, P(X=1) = 0.22,
P(X=2) = 0.25, P(X=3) = 0.25,
P(X=4) = 0.15, P(X=5) =
0.05
Find the expected value of X and the standard deviation of
X.

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).

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]?

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 data:
x
44
55
66
77
88
P(X=x)
0.20.
0.10
0.30.
0.20.
0.20.
Copy Data
Step 1 of 5:
Find the expected value E(X). Round your answer to one decimal
place.
Step 2 of 5: Find the variance
Step 3 of 5: Find the standard deviation
Step 4 of 5: Find the value of P(X>5). Round your answer to
one decimal place.
Step 5 of 5:
Step 5 of 5: Find the value of P(X<6). Round your...

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

The discrete random variable X has the following probability
distribution:
x
-10
0
5
10
p(x)
0.20
0.40
?
.10
Which one of the following correctly gives the value of the mean
and standard deviation of X? (explain/steps please)

Let X be a random variable with the following probability
distribution:
Value
x
of
X
P(X=x)
20
0.15
30
0.15
40
0.30
50
0.40
Find the expectation
E(X) and variance Var (X) of X.

Consider the following bivariate distribution p(x, y) of two
discrete random variables X and Y.
Y\X
-2
-1
0
1
2
0
0.01
0.02
0.03
0.10
0.10
1
0.05
0.10
0.05
0.07
0.20
2
0.10
0.05
0.03
0.05
0.04
a) Compute the marginal distributions p(x) and p(y)
b) The conditional distributions P(X = x | Y = 1)
c) Are these random variables independent?
d) Find E[XY]
e) Find Cov(X, Y) and Corr(X, Y)

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...

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