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12th Standard English Medium Maths Subject Probability Distributions Book Back 5 Mark Questions with Solution Part - II

12th Standard

    Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 25

    5 Marks

    5 x 5 = 25
  1. Suppose the amount of milk sold daily at a milk booth is distributed with a minimum of 200 Iitres and a maximum of 600 litres with probability density function 
    \(\begin{cases} \begin{matrix} k & 200\le x\le 600 \end{matrix} \\ \begin{matrix} 0 & otherwise \end{matrix} \end{cases}\) 
    Find
    (i) the value of k
    (ii) the distribution function
    (iii) the probability that daily sales will fall between 300 litres and 500 litres?

  2. If X is the random variable with probability density function f(x) given by,
    \(f(x)=\begin{cases} \begin{matrix} x+1 & -1\le x<0 \end{matrix} \\ \begin{matrix} -x+1 & 0\le x<1 \end{matrix} \\ \begin{matrix} 0 & otherwise \end{matrix} \end{cases}\) 
    then find
    (i) the distribution function F(x)
    (ii) P( -0.5 ≤X ≤ 0.5)

  3. If X is the random variable with distribution function F(x) given by,

    then find (i) the probability density function f(x) 
    (ii) P(0.3 ≤ X ≤ 0.6)

  4. A retailer purchases a certain kind of electronic device from a manufacturer. The manufacturer, indicates that the defective rate of the device is 5%. The inspector of the retailer randomly picks 10 items from a shipment. What is the probability that there will be
    (i) at least one defective item
    (ii) exactly two defective items.

  5. The mean and standard deviation of a binomial variate X are respectively 6 and 2.
    Find
    (i) the probability mass function
    (ii) P(X = 3)
    (iii) P(X\(\ge \)2).

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