1
MHT CET 2023 10th May Evening Shift
+2
-0

A fair die is tossed twice in succession. If $$\mathrm{X}$$ denotes the number of sixes in two tosses, then the probability distribution of $$\mathrm{X}$$ is given by

A
$$\mathrm{X=}x$$ 0 1 2
$$\mathrm{P(X=}x)$$ $$\frac{25}{36}$$ $$\frac{1}{36}$$ $$\frac{5}{18}$$
B
$$\mathrm{X=}x$$ 0 1 2
$$\mathrm{P(X=}x)$$ $$\frac{5}{18}$$ $$\frac{1}{36}$$ $$\frac{25}{36}$$
C
$$\mathrm{X=}x$$ 0 1 2
$$\mathrm{P(X=}x)$$ $$\frac{25}{36}$$ $$\frac{5}{18}$$ $$\frac{1}{36}$$
D
$$\mathrm{X=}x$$ 0 1 2
$$\mathrm{P(X=}x)$$ $$\frac{5}{18}$$ $$\frac{25}{36}$$ $$\frac{1}{36}$$
2
MHT CET 2023 10th May Morning Shift
+2
-0

For a binomial variate $$\mathrm{X}$$ with $$\mathrm{n}=6$$ if $$P(X=4)=\frac{135}{2^{12}}$$, then its variance is

A
$$\frac{8}{9}$$
B
$$\frac{1}{4}$$
C
4
D
$$\frac{9}{8}$$
3
MHT CET 2023 10th May Morning Shift
+2
-0

The p.d.f. of a discrete random variable is defined as $$\mathrm{f}(x)=\left\{\begin{array}{l} \mathrm{k} x^2, 0 \leq x \leq 6 \\ 0, \text { otherwise } \end{array}\right.$$

Then the value of $$F(4)$$ (c.d.f) is

A
$$\frac{30}{91}$$
B
$$\frac{30}{97}$$
C
$$\frac{15}{47}$$
D
$$\frac{15}{97}$$
4
MHT CET 2023 10th May Morning Shift
+2
-0

A player tosses 2 fair coins. He wins ₹5 if 2 heads appear, ₹ 2 if one head appears and ₹ 1 if no head appears. Then the variance of his winning amount in ₹ is :

A
6
B
$$\frac{5}{2}$$
C
$$\frac{9}{4}$$
D
$$\frac{17}{2}$$
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