Page 138 - DMTH404_STATISTICS

Statistics

Notes Moment: The rth moment of a discrete random variable about its mean is defined as:

n
r
r
 
  E X    X    p(X )
r i i
i 1

9.4 Self Assessment
1. If X is a .................... variable which can take values X , X , ..... X , with respective probabilities
1 2 n
as p(X ), p(X ), ...... p(X ), then its mean, also known as the Mathematical Expectation or
1 2 n
Expected Value of X, is given by:
n
E(X) = X p(X ) + X p(X ) + ...... + X p(X )   X p(X ) .
1 1 2 2 n n i i
i 1

(a) discrete random (b) variance
(c) continuous random (d) moment
2. The concept of .................... of a random variable or its probability distribution is also
similar to the concept of the variance of a frequency distribution.
(a) discrete random (b) variance
(c) continuous random (d) moment
3. If X is a .................... variable with probability density function p(X), then


E X
     X.p(X)dX
2
2
2
  E X        X    .p(X)dX
(a) discrete random (b) variance
(c) continuous random (d) moment

4. The rth .................... of a discrete random variable about its mean is defined as:
n
r
r
 
  E X    X    p(X )
i
i
r

i 1
(a) discrete random (b) variance
(c) continuous random (d) moment
9.5 Review Questions
1. Obtain the probability distribution of the number of aces in simultaneous throws of two
unbiased dice.
2. Explain the concept of a random variable and its probability distribution. Illustrate your
answer using experiment of the toss of two unbiased coins. Find the mean and variance of
the random variable defined by you for this experiment.
3. If E(X) = 1 and Var(X) = 5, find
2
(i) E[(2 + X) ]
(ii) Var(4 + 3X)

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