MHT CET 2025 19th April Morning Shift | Probability Question 34 | Mathematics

If a random variable $X$ has the p.d.f. $f(x)=\left\{\begin{array}{cc}\frac{\mathrm{k}}{x^2+1} & , \text { if } 0< x< \infty \\ 0 & , \text { otherwise }\end{array}\right.$ then c.d.f. of X is

$2 \tan ^{-1} x$

$\frac{\pi}{2} \tan ^{-1} x$

$\frac{2}{\pi} \tan ^{-1} x$

$\tan ^{-1} x$

MHT CET 2025 19th April Morning Shift

MCQ (Single Correct Answer)

-0

If a random variable $X$ follows the Binomial distribution $\mathrm{B}(33, \mathrm{p})$ such that $3 \mathrm{P}(\mathrm{X}=0)=\mathrm{P}(\mathrm{X}=1)$, then the variance of X is

$\frac{11}{144}$

$\frac{35}{48}$

$\frac{121}{48}$

$\frac{33}{144}$

MHT CET 2024 16th May Evening Shift

MCQ (Single Correct Answer)

-0

If a discrete random variable X is defined as follows

$\mathrm{P}[\mathrm{X}=x]=\left\{\begin{array}{cl}\frac{\mathrm{k}(x+1)}{5^x}, & \text { if } x=0,1,2 \ldots \ldots . \\ 0, & \text { otherwise }\end{array}\right.$

then $\mathrm{k}=$

$\frac{19}{25}$

$\frac{18}{25}$

$\frac{16}{25}$

$\frac{7}{25}$

MHT CET 2024 16th May Evening Shift

MCQ (Single Correct Answer)

-0

Numbers are selected at random, one at a time from two digit numbers $10,11,12 \ldots ., 99$ with replacement. An event $E$ occurs if and only if the product of the two digits of a selected number is 18 . If four numbers are selected, then probability that the event E occurs at least 3 times is

$\frac{87}{90^4}$

$\frac{348}{90^4}$

$87\left(\frac{4}{90}\right)^4$

$\left(\frac{4}{10}\right)^4$

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