Engineering Mathematics
Probability and Statistics
Practice questions from Probability and Statistics.
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IncorrectConsider discrete random variables and with probabilities as follows:
Given , the expected value of is
Given: and
Option (b) is correct.
Let and be continuous random variables with probability density functions and , respectively. Further, let and
Which one of the following options is correct?
Given: X and Y be two continuous random variables with Probability density function (PDF) and .
And,
For continuous Probability density function,
Option (a) is correct.
Let be a discrete random variable that is uniformly distributed over the set . Which of the following random variables is/are uniformly distributed?
Since X is uniformly distributed so probability of each symbol is equal to
Since all symbols except 0 occur twice in this sequence
(B)
Since all symbols occur only once in this sequence and hence this random variable is also uniformly distributed.
Else we can say that cubic function is one to one mapping so a uniformly distributed Random Variable is mapped to a uniformly distributed Random Variable.
(C)
The values 25,16,9,4,1 occur twice while rest of all the values occur only once so this is not an uniformly distributed random variable.
(D)
Since all symbols occur only once in this sequence and hence this random variable is also uniformly distributed.
Options (b) and (d) have no repeated samples.
One million random numbers are generated from a statistically stationary process with a Gaussian distribution with mean zero and standard deviation .
The is estimated by randomly drawing out 10,000 numbers of samples . The estimates are computed in the following two ways.
Since, there are 1 million random number but we are selecting 10000 random numbers out of 1 million. Hence. standard deviation is called Sample Standard Deviation.
Sample Variance for N samples
For 0 mean & 10000 samples
Three points in the -y plane are and . The value of the slope of the best fit straight line in the least square sense is __________ (Round off to 2 decimal places).
x | y |
-1 | 0.8 |
0 | 2.2 |
1 | 2.8 |
Mean of x co-ordinates
Mean of y co-ordinates
Slope of least square fit line
m = 1
The expected number of trials for first occurrence of a "head" in a biased coin is known to be 4. The probability of first occurrence of a "head" in the second trial is __________ (Round off to 3 decimal places).
∴ Coin is biased
If P (Head) = p then P(Tail) = 1 – p = q
Assume head occurs for first time on trial
For other (n-1) trial Tail must appear
