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Engineering Maths · all questions

Probability and Statistics
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Q61

Open question
The probability that a communication system will have high fidelity is 0.81. The probability that the system will have both high fidelity and high selectivity is 0.18. The probability that a given system with high fidelity will have high selectivity is

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Q62

Open question
Suppose A and B are two independent events with probabilities P(A) ≠ 0 and P(B) ≠ 0. Let and be their complements. Which one of the following statements is FALSE?

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Q63

Open question
Probability density function of a random variable X is given below
{\text{f}}\left( {\text{x}} \right) = \left[ {\begin{array}{*{20}{c}} {0.25}&{{\text{if }}1 \leqslant {\text{x}} \geqslant 5} \\ 0&{{\text{otherwise}}} \end{array}} \right]\,{\text{P}}\left( {{\text{X}} \leqslant 4} \right)

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Q64

Open question
A fail coin is tossed N times. The probability that head does not turn up in any of the tosses is

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Q65

Open question
There are 25 calculators in a box. Two of them are defective. Suppose 5 calculators are randomly picked for inspection (i.e., each has the same chance of being selected), what is the probability that only one of the defective calculators will be included in the inspection?

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Q66

Open question
A single dice is thrown twice. What is the probability that the sum is neither 8 nor 9?

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Q67

Open question
If P and Q are two random events, then the following is TRUE

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Q68

Open question
Four red balls, four green balls and four blue balls are put in a box. Three balls are pulled our of the box at random one after another without replacement. The probability that all the three balls are red is

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Q69

Open question
The chance of a student passing an exam is 20%. The chance of a student passing the exam and getting above 90% marks in it is 5%. Given that a student passes the examination, the probability that the student gets above 90% marks is

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Q70

Open question
A program consists of two modules executed sequentially. Let f1(t) and f2(t) respectively denote the probability density functions of time taken to execute the two modules. The probability density function of the overall time taken to execute the program is given by

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Q71

Open question
The random variable X takes on the values 1, 2 (or) 3 with probabilities    and  respectively the values of P and E(X) are respectively.

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Q72

Open question
There are two containers, with one containing 4 red and 3 green balls and the other containing 3 blue and 4 green balls. One ball is drawn at random from each container. The probability that one of the balls is red and the other is blue will be

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Q73

Open question
A fair coin is tossed independently four times. The probability of the event "the number of times heads show up is more than the number of times tails show up" is

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Q74

Open question
Assume that the duration in minutes of a telephone conversion follows the expo-nential distribution    The probability that the conversion will exceed five minutes is

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Q75

Open question
A fair coin is tossed three times in succession. If the first toss produces a head, then the probability of getting exactly two heads in three tosses is

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Q76

Open question
Marks obtained by 100 students in an examination are given in the table:
Sr. No. Marks obtained No. of students
    1           25           20
    2           30           20
    3           35           40
    4           40           20

What would be mean, median and mode of marks obtained by the students?

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Q77

Open question
If X is a normal variable with mean 30 and standard deviation 5, what is probability (26 ≤ X ≤ 34), given A(z = 0.8) = 0.2881?

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Q78

Open question
If f(x) and g(x) are two probability density functions,
{\text{f}}\left( {\text{x}} \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{{\text{x}}}{{\text{a}}} + 1}&:&{ - {\text{a}} \leqslant {\text{x}} < 0} \\ { - \frac{{\text{x}}}{{\text{a}}} + 1}&:&{0 \leqslant {\text{x}} \leqslant {\text{a}}} \\ 0&:&{{\text{otherwise}}} \end{array}} \right.;\,\,{\text{g}}\left( {\text{x}} \right) = \left\{ {\begin{array}{*{20}{c}} { - \frac{{\text{x}}}{{\text{a}}}}&:&{ - {\text{a}} \leqslant {\text{x}} < 0} \\ {\frac{{\text{x}}}{{\text{a}}}}&:&{0 \leqslant {\text{x}} \leqslant {\text{a}}} \\ 0&:&{{\text{otherwise}}} \end{array}} \right.
Which one of the following statements is true?

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Q79

Open question
If three coins are tossed simultaneously, the probability of getting at least one head is

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Q80

Open question
Consider a random variable to which a Poisson distribution is best fitted. It happens that P(x = 1) = P(x = 2) on this distribution plot. The variance of this distribution will be

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