Probability and Statistics - Engineering Mathematics - Biomedical Engineering Previous Year Questions

1

2020 · Biomedical Engineering · Engineering Mathematics · Probability and Statistics

Biomedical Engineering (BM) 2020

A continuous random variable \(x\) has a probability density function given by \(f(x) = e^{-\alpha|x|}\) \((-\infty < x < \infty)\) where \(\alpha\) is a real constant. The variance of \(x\) is ______ (correct up to one decimal place).

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2

2020 · Biomedical Engineering · Engineering Mathematics · Probability and Statistics

Biomedical Engineering (BM) 2020

A gynaecologist recorded the blood pressure (BP) of patients as shown in the Table below. Using Regression process, the diastolic BP of a 38 year old patient (mm Hg) is __________ (rounded off to two decimal places).

Age (years)	23	24	25	26	28	29	31	35	40
BP (diastolic) mm Hg	65	60	62	70	70	73	75	83	90

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3

2021 · Biomedical Engineering · Engineering Mathematics · Probability and Statistics

Biomedical Engineering (BM) 2021

For \(f_X(x) = \frac{1}{\pi} \left( \frac{q}{e^x + e^{-x}} \right)\) to be a valid probability distribution function of a random variable X, the value of q is _____.

A

2

B

\(\pi\)

C

4

D

\(-\pi\)

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4

2021 · Biomedical Engineering · Engineering Mathematics · Probability and Statistics

Biomedical Engineering (BM) 2021

A drug manufacturer believes that there is a 95% chance that the drug controller will approve a new drug the company plans to distribute if the results of the current testing show that the drug causes no side effects. The manufacturer further believes that there is a 0.50 probability that the drug will be approved even if the test shows side effects. A physician working for the drug manufacturer believes there is a 0.20 probability that tests will show side effects. If the drug is approved by the drug controller, the probability that the drug causes side effects is ______. (rounded off to three decimal places)

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5

2022 · Biomedical Engineering · Engineering Mathematics · Probability and Statistics

Biomedical Engineering (BM) 2022

Due to the current COVID pandemic conditions, assume that positive or negative status of any individual are equally likely. There are 3 members in a family. If one of the members has tested COVID positive, the conditional probability that at least 2 members are COVID positive is ______ (rounded off to three decimal places).

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6

2022 · Biomedical Engineering · Engineering Mathematics · Probability and Statistics

Biomedical Engineering (BM) 2022

In a biological study, the experimental values measured from 6 subjects are given in the table below. Using this data, the linear regression coefficient for estimating the weight of the heart based on the systolic pressure is _______ (rounded off to two decimal places).

Systolic pressure (in mm Hg)	120	90	100	110	140	130
Weight of the heart (in g)	500	300	420	390	490	450

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7

2023 · Biomedical Engineering · Engineering Mathematics · Probability and Statistics

Biomedical Engineering (BM) 2023

What is the magnitude of the difference between the mean and the median of the dataset {1, 2, 3, 4, 6, 8}?

A

0

B

1

C

0.5

D

0.25

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8

2023 · Biomedical Engineering · Engineering Mathematics · Probability and Statistics

Biomedical Engineering (BM) 2023

For a Binomial random variable X, E(X) and Var(X) are the expectation and variance, respectively. Which one of the following statements CANNOT be true?

A

E(X) = 20 and Var(X) = 16

B

E(X) = 6 and Var(X) = 5.4

C

E(X) = 10 and Var(X) = 15

D

E(X) = 64 and Var(X) = 12.8

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9

2024 · Biomedical Engineering · Engineering Mathematics · Probability and Statistics

Biomedical Engineering (BM) 2024

A group of four people were residing together when a new virus was detected. If the probability of each person being infected is 0.1, then the probability that at least two of them are infected is _____. Give your answer rounded off to 3 decimal places.

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10

2024 · Biomedical Engineering · Engineering Mathematics · Probability and Statistics

Biomedical Engineering (BM) 2024

A random noise signal with Gaussian distribution has a mean of zero and a standard deviation of 1 mV. The probability that an instantaneous measurement of this signal is greater than 2 mV or lesser than -2 mV is _____. Give your answer as a percentage rounded off to the nearest integer.

A

[Waveform A]

B

[Waveform B]

C

[Waveform C]

D

[Waveform D]

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11

2025 · Biomedical Engineering · Engineering Mathematics · Probability and Statistics

Biomedical Engineering (BM) 2025

The elements of the dataset \( \{-5, 1, a, 5, b\} \) are in ascending order. If both mean and median of the dataset are equal to 3, what is the value of \( b \)?

A

7

B

11

C

9

D

12

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12

2025 · Biomedical Engineering · Engineering Mathematics · Probability and Statistics

Biomedical Engineering (BM) 2025

N independent trials of a binomial random variable yield an expectation value of 16 and variance of 12. What is the value of N?

A

80

B

60

C

45

D

64

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13

2026 · Biomedical Engineering · Engineering Mathematics · Probability and Statistics

Biomedical Engineering (BM) 2026

X is a random variable whose mean is 3 and standard deviation is 2. A new random variable Y is defined as: \( Y = \frac{X-3}{4} \) The standard deviation of Y is ____

A

0.5

B

1

C

2

D

8

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14

2026 · Biomedical Engineering · Engineering Mathematics · Probability and Statistics

Biomedical Engineering (BM) 2026

A biased coin has a probability of heads equal to 1/3 and a probability of tails equal to 2/3. A binary random variable X assumes a value 1 for heads and -1 for tails. The variance of X is ______

A

1/3

B

5/9

C

8/9

D

1

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15

2026 · Biomedical Engineering · Engineering Mathematics · Probability and Statistics

Biomedical Engineering (BM) 2026

Which of the following conditions result(s) in a higher statistical power for comparing means of two samples using t-test?

A

An increase in the sizes of both the samples from 100 to 1000

B

An increase in the significance level from \(\alpha = 0.01 \) to \(\alpha = 0.2 \)

C

A decrease in the significance level from \(\alpha = 0.2 \) to \(\alpha = 0.01 \)

D

A decrease in the sizes of both the samples from 1000 to 100

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