71. The random variable X takes on the values 1, 2 (or) 3 with probabilities $$\frac{{2 + 5{\text{P}}}}{5},\frac{{1 + 3{\text{P}}}}{5}$$ and $$\frac{{1.5 + 2{\text{P}}}}{5}$$ respectively the values of P and E(X) are respectively.
72. There are two containers, with one containing 4 red and 3 green balls and the other containing 3 blue and 4 green balls. One ball is drawn at random from each container. The probability that one of the balls is red and the other is blue will be
73. A fair coin is tossed independently four times. The probability of the event "the number of times heads show up is more than the number of times tails show up" is
74. Assume that the duration in minutes of a telephone conversion follows the expo-nential distribution $${\text{f}}\left( {\text{x}} \right) = \frac{1}{5}{{\text{e}}^{ - \frac{{\text{x}}}{5}}},\,{\text{x}} \geqslant {\text{0}}{\text{.}}$$ The probability that the
conversion will exceed five minutes is
75. A fair coin is tossed three times in succession. If the first toss produces a head, then the probability of getting exactly two heads in three tosses is
76. Marks obtained by 100 students in an examination are given in the table:
Sr. No.
Marks obtained
No. of students
1
25
20
2
30
20
3
35
40
4
40
20
What would be mean, median and mode of marks obtained by the students?
| Sr. No. | Marks obtained | No. of students |
| 1 | 25 | 20 |
| 2 | 30 | 20 |
| 3 | 35 | 40 |
| 4 | 40 | 20 |
What would be mean, median and mode of marks obtained by the students?
77. If X is a normal variable with mean 30 and standard deviation 5, what is probability (26 ≤ X ≤ 34), given A(z = 0.8) = 0.2881?
78. If f(x) and g(x) are two probability density functions,
\[{\text{f}}\left( {\text{x}} \right) = \left\{ {\begin{array}{*{20}{c}}
{\frac{{\text{x}}}{{\text{a}}} + 1}&:&{ - {\text{a}} \leqslant {\text{x}} < 0} \\
{ - \frac{{\text{x}}}{{\text{a}}} + 1}&:&{0 \leqslant {\text{x}} \leqslant {\text{a}}} \\
0&:&{{\text{otherwise}}}
\end{array}} \right.;\,\,{\text{g}}\left( {\text{x}} \right) = \left\{ {\begin{array}{*{20}{c}}
{ - \frac{{\text{x}}}{{\text{a}}}}&:&{ - {\text{a}} \leqslant {\text{x}} < 0} \\
{\frac{{\text{x}}}{{\text{a}}}}&:&{0 \leqslant {\text{x}} \leqslant {\text{a}}} \\
0&:&{{\text{otherwise}}}
\end{array}} \right.\]
Which one of the following statements is true?
\[{\text{f}}\left( {\text{x}} \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{{\text{x}}}{{\text{a}}} + 1}&:&{ - {\text{a}} \leqslant {\text{x}} < 0} \\ { - \frac{{\text{x}}}{{\text{a}}} + 1}&:&{0 \leqslant {\text{x}} \leqslant {\text{a}}} \\ 0&:&{{\text{otherwise}}} \end{array}} \right.;\,\,{\text{g}}\left( {\text{x}} \right) = \left\{ {\begin{array}{*{20}{c}} { - \frac{{\text{x}}}{{\text{a}}}}&:&{ - {\text{a}} \leqslant {\text{x}} < 0} \\ {\frac{{\text{x}}}{{\text{a}}}}&:&{0 \leqslant {\text{x}} \leqslant {\text{a}}} \\ 0&:&{{\text{otherwise}}} \end{array}} \right.\]
Which one of the following statements is true?
79. If three coins are tossed simultaneously, the probability of getting at least one head is
80. Consider a random variable to which a Poisson distribution is best fitted. It happens that P(x = 1) = $$\frac{2}{3}$$P(x = 2) on this distribution plot. The variance of this distribution will be
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