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AMU MCA Previous Year Questions (PYQs)

AMU MCA Probability PYQ

AMU MCA PYQ
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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AMU MCA Previous Year PYQ AMU MCA AMU MCA 2020 PYQ

Solution

Level of significance:

$\alpha = P(X \ge 1 \mid \theta=2)$

$= \int_{1}^{\infty} 2e^{-2x} dx$

$= \left[-e^{-2x}\right]_{1}^{\infty}$

$= e^{-2}$

$= \frac{1}{e^2}$

AMU MCA PYQ
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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AMU MCA Previous Year PYQ AMU MCA AMU MCA 2020 PYQ

Solution

Total items = 100

Probability both defective:

$=\frac{20}{100}\times\frac{19}{99}$

$=\frac{380}{9900}=\frac{19}{495}$

AMU MCA PYQ
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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AMU MCA Previous Year PYQ AMU MCA AMU MCA 2020 PYQ

Solution

$t=\frac{\bar{d}}{s_d/\sqrt{n}}$

$=\frac{15}{5/\sqrt{9}}=\frac{15}{5/3}=\frac{15\times3}{5}=9$

AMU MCA PYQ
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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AMU MCA Previous Year PYQ AMU MCA AMU MCA 2020 PYQ

Solution

Standard error of sample proportion:

$SE=\sqrt{\frac{PQ}{n}}$

AMU MCA PYQ
In simple random sampling without replacement, the probability that a specified unit of the population will be included in the sample (Here $n$ denotes sample size and $N$ denotes population size) is:





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AMU MCA Previous Year PYQ AMU MCA AMU MCA 2025 PYQ

Solution

In simple random sampling, each unit has equal chance. Probability of inclusion $= \frac{\text{sample size}}{\text{population size}} = \frac{n}{N}$.

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