1. An urn contains 5 red balls and 5 black balls. In the first draw, one ball is picked at random and discarded without noticing its colour. The probability to get a red ball in the second draw is
2. A bag contains 7 red and 4 white balls. Two balls are drawn at random. What is the probability that both the balls are red?
3. Consider the continuous random variable with probability density function
f(t) = 1 + t for -1 ≤ t ≤ 0
= 1 - t for 0 ≤ t ≤ 1
The standard deviation of the random variable is
f(t) = 1 + t for -1 ≤ t ≤ 0
= 1 - t for 0 ≤ t ≤ 1
The standard deviation of the random variable is
4. A continuous random variable X has a probability density function f(x) = e-x, 0 < x < $$\infty $$ . Then P{X > 1} is
5. A deck of 5 cards (each carrying a distinct number from 1 to 5) is shuffled thoroughly. Two cards are then remove done at a time from the deck. What is the probability that the two cards are selected with the number on the first card being one higher than the number on the second card?
6. A random variable X has the density function $${\text{f}}\left( {\text{x}} \right) = {\text{K}}\frac{1}{{1 + {{\text{x}}^2}}},$$ where $$ - \infty $$ < x < $$\infty $$ . The value of K is
7. A normal random variable X has following probability density function $${{\text{f}}_{\text{x}}}\left( {\text{x}} \right) = \frac{1}{{\sqrt {8\pi } }}{{\text{e}}^{ - \left\{ {\frac{{{{\left( {{\text{x}} - 1} \right)}^2}}}{8}} \right\}}},\, - \infty < {\text{x}} \leqslant \infty .$$
Then $$\int\limits_1^\infty {{{\text{f}}_{\text{x}}}\left( {\text{x}} \right){\text{dx}}} $$ is
Then $$\int\limits_1^\infty {{{\text{f}}_{\text{x}}}\left( {\text{x}} \right){\text{dx}}} $$ is
8. Consider a random variable X that takes values +1 and -1 with probability 0.5 each. The values of the cumulative distribution function F(x) at X = -1 and +1 are
9. A box contains 25 parts of which 10 are defective. Two parts are being drawn simultaneously in a random manner from the box. The probability of both the parts being good is
10. An urn contains 5 red and 7 green balls. A ball is drawn at random and its colour is noted. The ball is placed back into the urn along with another ball of the same colour. The probability of getting a red ball in the next draw is
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