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Probability Distributions 3 Mark Book Back Question Paper With Answer Key

12th Standard

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Maths

Time : 00:45:00 Hrs
Total Marks : 27

    3 Marks

    9 x 3 = 27
  1. Suppose X is the number of tails occurred when three fair coins are tossed once simultaneously. Find the values of the random variable X and number of points in its reverse images.

  2. The probability density function of X is given by \(f(x)=\begin{cases} \begin{matrix} kxe^{ -2x } & forx>0 \end{matrix} \\ \begin{matrix} 0 & for\quad x\le 0 \end{matrix} \end{cases}\) Find the value of k.

  3. An urn contains 2 white balls and 3 red balls. A sample of 3 balls are chosen at random from the urn. If X denotes the number of red balls chosen, find the values taken by the random variable X and its number of inverse images

  4. Two balls are chosen randomly from an urn containing 6 white and 4 black balls. Suppose that we win Rs. 30 for each black ball selected and we lose Rs. 20 for each white ball selected. If X denotes the winning amount, then find the values of X and number of points in its inverse images.

  5. Two fair coins are tossed simultaneously (equivalent to a fair coin is tossed twice). Find the probability mass function for number of heads occurred.

  6. Find the mean and variance of a random variable X , whose probability density function is \(f(x)=\begin{cases} \begin{matrix} { \lambda e }^{ -2x } & for\ge 0 \end{matrix} \\ \begin{matrix} 0 & otherwise \end{matrix} \end{cases}\)

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