Mining Engineering
GATE MN topic:probability-and-statistics PYQs
Build your understanding with focused practice from past exam papers.
Questions 11–20 of 26. Imported answers require independent review unless marked reviewed.
Question 14
Open questionMNMCQ1 markNeeds review
Variance of the sum of two statistically independent random variables
and
,
, isYour answerChoose one option.
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Open questionMNMCQ2 marksNeeds review
In order to check whether iron ore is supplied to the specification of 62% Fe, a steel company has conducted a hypothesis test with the null hypothesis as H₀: μFe = 62% and alternative hypothesis Ha: μFe < 62%. A random sample of 5 observations reveal the following grade values of the lot, 58%, 56%, 60%, 64%, 62%. The t-test statistic for the hypothesis is
Your answerChoose one option.
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Open questionMNNAT2 marksNeeds review
Injury experience is studied in an underground coal mine with a random sample of 132 workers. The results of the study are tabulated below.
| Injured | Non-injured | Total workers |
|---|---|---|---|
Roof-bolter operators | 13 | 12 | 25 |
Loader operators | 35 | 72 | 107 |
Total workers | 48 | 84 | 132 |
The odds ratio of experiencing an injury by the roof-bolter operators when compared to the loader operators is ______. [round off to 2 decimal places]
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Open questionMNNAT2 marksNeeds review
A random variable
is defined by
The value of
is ______. [round off to one decimal place]Log in to check the answer
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Open questionMNNAT1 markNeeds review
A random variable
has the following probability mass function. | 3 | 6 | 8 | 12 |
|---|---|---|---|---|
| 1/2 | 1/4 | 1/8 | 1/8 |
The expected value of the variable
is __________ (round off to 1 decimal place).Log in to check the answer
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Open questionMNNAT1 markNeeds review
A random sample has five observations as shown below.
| 11 | 14 | 15 | 13 | 12 |
The coefficient of variation of the sample is __________ (round off to 3 decimal places).
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If the sample statistic
is an unbiased estimator of the parameter
, thenYour answerChoose one option.
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The coefficient of variation of a dataset is defined as
Your answerChoose one option.
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Open questionMNNAT2 marksNeeds review
The random variable X has probability density function as given by
The value E(X
) (rounded off to one decimal place) is _____.Log in to check the answer
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Open questionGAMCQ2 marksNeeds review
A six sided unbiased die with four green faces and two red faces is rolled seven times. Which of the following combinations is the most likely outcome of the experiment?
Your answerChoose one option.
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