No.  Problems & Solutions [Click Hide/Show to display the solutions below the question]  

01. 
Find the mean and variance of the following probability distribution and hence find its standard deviation
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02. 
A bakery has the following schedule of daily demand for cakes.
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03. 
A random variable x has the following probability distribution
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04. 
The monthly demand for radios is known to have the following probability distribution
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05. 
For what value of "a" will the function f(x) = ax; x = 1, 2, ..., n be the probability mass function of a discrete random variable x? find the mean and the variance of x.
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06. 
Evaluate K if f(x) = K, x = 1, 2, 3, 4, 5, 6; f(x) = 0, elsewhere is a probability mass function. Also find its mean and standard deviation.
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07. 
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08. 
The range of a random variable X is (0, 1, 2). If C is a constant such that P(X) = 3C^{3}, P(X = 1) = 4C − 10C^{2}, P(x = 2) = 5C − 1, then C =
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09. 
The value of C for which P(X = K) = CK^{2} can serve as the probability function of a random variable x that takes values 0, 1, 2, 3, 4, is ...
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10. 
A random variable x takes the values of &m inus;1, 0, 1. Its mean is 0.6. If P(X = 0) = 0.2, then P(X = 1) = ?
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11. 
If x is a random variable, show that (i) E(1) = 1; (ii) E(3x) = 3E(x) and (iii) E(2 + 3x) = 2 + 3E(x)
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12. 
Prove that: (i) var(2) = 0, (ii) var(3x) = 9 (iii) var (x + 4x) = 16 var (x)
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13. 
If the variance of a random variable x is 5, then the variance of the random variable
(− 3x) is
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14. 
A number is chosen at random from the set 1, 2, 3, ... , 100 and another number is chosen at random from the set 1, 2, 3, ... , 50. What is the expected value of the sum and the expected value of the product?
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15. 
The probability that there is at least one error is an accounts statement prepared by A is 0.2 and for B and C they are 0.25 and 0.4 respectively A, B, and C prepared 10, 16 and 20 statements respectively. Find the expected number of correct statements in all
Solution

No.  Problems for Practice 

01.  If it rains, an umbrella sales man can earn Rs. 300 per day. If it is fair he can lose Rs. 60 per day. What is his expectation if the probability of rain is 0.3? 
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