1
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

A random variable $X$ has the following probability distribution

$\mathrm{X:}$ 1 2 3 4 5
$\mathrm{P(X):}$ $\mathrm{k^2}$ $\mathrm{2k}$ $\mathrm{k}$ $\mathrm{2k}$ $\mathrm{5k^2}$

Then $\mathrm{P(X > 2)}$ is equal to

A
$\frac{7}{12}$
B
$\frac{23}{36}$
C
$\frac{1}{36}$
D
$\frac{1}{6}$
2
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability, that a student will get 4 or more correct answers just by guessing, is

A
$\frac{10}{3^5}$
B
$\frac{17}{3^5}$
C
$\frac{13}{3^5}$
D
$\frac{11}{3^5}$
3
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let a random variable X have a Binomial distribution with mean 8 and variance 4 . If $\mathrm{P}(x \leqslant 2)=\frac{\mathrm{k}}{2^{16}}$, then k is equal to

A
17
B
121
C
1
D
137
4
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

For the probability distribution

$\mathrm{X:}$ $-2$ $-1$ $0$ $1$ $2$ $3$
$\mathrm{p}(x):$ 0.1 0.2 0.2 0.3 0.15 0.05

Then the $\operatorname{Var}(\mathrm{X})$ is

(Given : $$\left.(0.25)^2=0.0625,(0.35)^2=0.1225,(0.45)^2=0.2025\right)$$

A
0.8275
B
1.1225
C
1.8275
D
2.0725
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