MTH302

1. Which of the following is correct?

(a) Var(x) = E(x) - E(x') (b) Var(x) = E(x²) - E(x) (c) Var(x) = E(x²) - [E(x)]² (d) Var(x) = [E(x) - E(x²)]

2. Two events A and B are ________ if the occurrence (or non-occurrence) of one event has no effect on the probability of the occurrence (or non-occurrence) of the other event. Which of the following best completes the previous sentence?

(a) statistically independent (b) mutually exclusive (c) statistically dependent (d) none of the above

3. The random variable X has the following distribution:

X	P(x)
10	0.2
20	0.3
30	0.5

Find P(X = 10):

(a) 0.2 (b) 0.5 (c) 0.3 (d) 0.1

4. Given E(X) = 5 and E(Y) = -2, then E(X - Y) is:

(a) 3 (b) 5 (c) 7 (d) -2

5. The height of persons in a country is a random variable of the type:

(a) Discrete random variable (b) Continuous random variable (c) Both (a) and (b) (d) Neither (a) and (b)

6. A random variable X has the following probability function:

X	P(x)
0	K
1	2K
2	2K
3	3K
4	K²
5	2K² + K

Find K:

(a) 1/10 (b) 2/7 (c) 3/10 (d) 4/5

7. Var(aX + b) is:

(a) ab Var(X) (b) a² Var(X) (c) a Var(X) (d) a² Var(X) + b

8. A discrete random variable X has the following probability distribution:

X	P(x)
1	0.2
2	0.3
3	0.4
4	0.1

Find the variance Var(X) of X:

(a) 6.96 (b) 7.96 (c) 9.69 (d) 5.69

9. If a random variable X has a probability density function ( f(x) = ax(2 - x) ), ( 0 < x < 2 ), then the value of a is:

(a) 3/4 (b) 1/4 (c) 2 (d) 1/2

10. If a random variable X has a probability mass function ( P(X = x) = k(2/3)^x, ( x = 1, 2, 3, ...), then the value of the constant k is:

(a) 3/4 (b) 2/3 (c) 1/2 (d) 1/4

Math MCQs

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