1
GATE CE 2022 Set 2
Numerical
+2
-0

A pair of six-faced dice is rolled twice. The probability that the sum of the outcomes in each roll equals 4 in exactly two of the three attempts is _________ (round off to three decimal places).

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2
GATE CE 2017 Set 1
MCQ (Single Correct Answer)
+2
-0.6
For the function $$\,f\left( x \right) = a + bx,0 \le x \le 1,\,\,$$ to be a valid probability density function, which one of the following statements is correct?
A
$$a = 1,\,b = 4$$
B
$$\,a = 0.5,\,b = 1$$
C
$$a=0,$$ $$b=1$$
D
$$a=1,$$ $$b=-1$$
3
GATE CE 2016 Set 2
MCQ (Single Correct Answer)
+2
-0.6
If $$f(x)$$ and $$g(x)$$ are two probability density functions, $$$f\left( x \right) = \left\{ {\matrix{ {{x \over a} + 1} & : & { - a \le x < 0} \cr { - {x \over a} + 1} & : & {0 \le x \le a} \cr 0 & : & {otherwise} \cr } } \right.$$$ $$$g\left( x \right) = \left\{ {\matrix{ { - {x \over a}} & : & { - a \le x < 0} \cr {{x \over a}} & : & {0 \le x \le a} \cr 0 & : & {otherwise} \cr } } \right.$$$

Which of the following statements is true?

A
Mean of $$f(x)$$ and $$g(x)$$ are same; Variance of $$f(x)$$ and $$g(x)$$ are same .
B
Mean of $$f(x)$$ and $$g(x)$$ are same ; Variance of $$f(x)$$ and $$g(x)$$ are different.
C
Mean of $$f(x)$$ and $$g(x)$$ are different ; Variance of $$f(x)$$ and $$g(x)$$ are same .
D
Mean of $$f(x)$$ and $$g(x)$$ are different; Variance of $$f(x)$$ and $$g(x)$$ are different.
4
GATE CE 2015 Set 1
Numerical
+2
-0
Consider the following probability mass function (p.m.f) of a random variable $$X.$$ $$$p\left( {x,q} \right) = \left\{ {\matrix{ q & {if\,X = 0} \cr {1 - q} & {if\,X = 1} \cr 0 & {otherwise} \cr } } \right.$$$
$$q=0.4,$$ the variance of $$X$$ is _______.
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