STATISTICAL INFERENCE & QUANTITATIVE RESEARCH
Spring-2022
ASSIGNMENT # 01
Construct the probability distribution based on the following frequency distribution:
OUTCOMES:
102
FREQUENCIES: 10
105
20
108
45
111
15
114
20
117
15
(a) Draw the Histogram graph of the probability distribution.
(b) Compute the expected value of the outcomes.
(c) Compute the Variance and Standard Deviation of the probability distribution.
A coin is biased such that a HEAD is three times as likely to occurs as a TAIL. Find the expected TAILSwhen
this coin is tossed thrice.
Let X be the random Variable with the following probability distribution:
X:
P(X):
3
1/6
6
1/2
(a) Compute E(X).
(b) Compute E(X2)
(c) Compute E(1/√X)
9
1/3
(d) Compute E[1/2(5X - 7)]
(e) Compute E(5X - 13)2
(f) Compute E(X + 1)3
Let X be the random variable and has the following probability distribution:
X:
P(X) :
1
A
5
B
9
C
Where A, B, C are any constants. It is also known that P(X < 4) = P(X > 4) and P(X ≤ 5) = 2P(X > 5).
Find the values of A, B and C.
Find the value of K such that the following are the probability distributions:
(a) P(X) = K/X3 where X = 1, 2, 3, 4
(b) P(X) = KX2 where X = 0.5, 0.25, 0.75
Also Compute the Mean and Variance of the above distributions.
BEST OF LUCK
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