AMU MCA Probability Previous Year Questions (PYQs) – Page 1 of 2
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Showing 13 questions
If $x \ge 1$ is the critical region for testing $H_0:\theta=2$ against $H_1:\theta=1$, on the basis of a single observation from the population
$f(x;\theta)=\theta e^{-\theta x},\quad x \ge 0$
then the value of the level of significance is
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Solution
Level of significance:
$\alpha = P(X \ge 1 \mid \theta=2)$
$= \int_{1}^{\infty} 2e^{-2x} dx$
$= \left[-e^{-2x}\right]_{1}^{\infty}$
$= e^{-2}$
$= \frac{1}{e^2}$
A lot consists of 20 defective and 80 non-defective items. Two items are drawn at random without replacement. What is the probability that both items are defective?
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Solution
Total items = 100
Probability both defective:
$=\frac{20}{100}\times\frac{19}{99}$
$=\frac{380}{9900}=\frac{19}{495}$
The mean difference between 9 paired observations is 15, and the standard deviation of differences is 5. The value of statistic $t$ is
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Solution
$t=\frac{\bar{d}}{s_d/\sqrt{n}}$
$=\frac{15}{5/\sqrt{9}}=\frac{15}{5/3}=\frac{15\times3}{5}=9$
Two persons $A$ and $B$ take turns in throwing a pair of dice. The first person to throw $9$ from both dice will be awarded the prize. If $A$ throws first, then the probability that $B$ wins
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The probability that in a year of the $22^{\text{nd}}$ century chosen at random, there will be $53$ Sundays, is
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Solution
If $P$ is the population proportion of some characteristic under study,
$Q=1-P$ and $n$ is the sample size, then the standard error of observed sample proportion is
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Solution
Standard error of sample proportion:
$SE=\sqrt{\frac{PQ}{n}}$
If four whole numbers taken at random are multiplied together, then the probability that the last digit in the product is $1,3,7,$ or $9$ is
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If $A_i\ (i=1,2,\ldots,n)$ are $n$ independent events, with $P(A_i)=1-\frac{1}{2^i}$, then the probability that atleast one of the $n$ events occurs, is
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Let $A$ be an event that a family has children of both sexes and $B$ be the event that the family has atmost one boy. If the family has $3$ children then the events $A$ and $B$ are
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Solution
A fair coin is tossed $n$ times. Let the random variable $X$ denote the number of times the head occurs. If $P[X=1],\ P[X=2]$ and $P[X=3]$ are in arithmetic progression (AP), then the number $n$ of independent trial is
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Solution
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