A player tosses 2 fair coins. He with Rs. 5 if 2 heads appear, Rs. 2 if 1 head appears and Rs. 1 if no head…

A player tosses 2 fair coins. He with Rs. 5 if 2 heads appear, Rs. 2 if 1 head appears and Rs. 1 if no head appear, then the variance of his winning amount is
  1. $\frac{9}{4}$
  2. 6
  3. $\frac{5}{2}$
  4. $\frac{17}{2}$

Solution

Variance $=\sum p_i x_i{ }^2-\left(\sum p_i x_i\right)^2$ $=\frac{17}{2}-\frac{25}{4}=\frac{9}{4}$

Asked in: MHT CET 2022 (08 Aug Shift 1)

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