MCQs of Basic Probability (Probability and Statistics - 3130006)

Probability and Statistics (3130006) MCQs

MCQs of Basic Probability

Showing 101 to 108 out of 108 Questions

101.

f(x,y) is called joint probability density function of (x,y) provided _______.

(a)	f(x,y)>0 for all x,y
(b)	f(x,y)≥0 for all x,y
(c)	f(x,y)<0 for all x,y
(d)	none of the above

102.

Two random variables X and Y are independent if _______.

(a)	$P (X = x, Y = y) = P_{X} (x) \cdot P_{Y} (y) if X & Y are discrete$
(b)	$f (x, y) = F_{X} (x) \cdot F_{Y} (y) if X & Y are continuous$
(c)	both of above
(d)	none of the above

103.

If joint probability mass function is $P (x, y) = k (2 x + 3 y); x = 0, 1, 2 and y = 1, 2, 3 .$ Then k=_______.

(a)	$\frac{1}{36}$
(b)	$\frac{1}{72}$
(c)	$\frac{1}{18}$
(d)	$\frac{1}{9}$

104.

If joint probability mass function is $P (x, y) = k (2 x + 3 y); x = 0, 1, 2 and y = 1, 2, 3 .$ Then $P (x \leq 1, y \geq 2) =$ _______.

(a)	$\frac{34}{72}$
(b)	$\frac{68}{36}$
(c)	$\frac{1}{72}$
(d)	$\frac{34}{36}$

105.

If joint probability mass function is $P (x, y) = k (2 x + 3 y); x = 0, 1, 2 and y = 1, 2, 3 .$ Then $E (x) =$ _______.

(a)	1.6671
(b)	1.6667
(c)	1.6716
(d)	1.6761

106.

For probability density function $f (x, y) = \{\begin{cases} \frac{3}{4} + xy; & 0 \leq x < 1 & 0 \leq y < 1 \\ 0; & o t h e r w i s e \end{cases}$ , joint probability is _______.

(a)	0
(b)	0.5
(c)	1
(d)	none of the above

107.

If $f (x, y) = \{\begin{cases} cxy; & 0 < x < 4 & 1 < y < 5 \\ 0; & o t h e r w i s e \end{cases}$ is a joint probability density function then $c =$ _______.

(a)	$\frac{4}{96}$
(b)	$\frac{3}{96}$
(c)	$\frac{2}{96}$
(d)	$\frac{1}{96}$

108.

For joint probability density function $f (x, y) = x^{2} \cdot y^{3}; 0 < x < 1 & 0 < y < x$ ,what is expected value of x?

(a)	$\frac{4}{32}$
(b)	$\frac{1}{32}$
(c)	$\frac{2}{32}$
(d)	$\frac{3}{32}$

Showing 101 to 108 out of 108 Questions