A hydraulic structure has four gates which operate independently. The probability of failure of each gate is 0.2. Given that gate 1 has failed, the probability that both gates 2 and 3 will fail is
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Engineering Maths · all questionsProbability and Statistics
Probability and Statistics
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A fair dice is tossed two times. The probability that the second toss results in a value that is higher than the first toss is
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Consider the finite sequence of random values X = [x1, x2, ... , xn]. Let μx be the mean and σx be the standard deviation of X. Let another finite sequence Y of equal length be derived from this as yi = a ∗ xi + b, where a and b are positive constant. Let μy be the mean and σy be the standard deviation of this sequence. Which one of the following statements INCORRECT?
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Two fair dice are rolled and the sum r of the numbers turned up is considered
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Two coins R and S are tossed. The 4 joint events HRHS, TRTS, HRTS, TRHS have probabilities 0.28, 0.18, 0.30, 0.24, respectively, where H represents head and T represents tail. Which one of the following is TRUE?
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If {x} is a continuous, real valued random variable defined over the interval (-, +) and its occurrence is defined by the density function given as:
where 'a' and 'b' are the statistical attributes of the random variable {x}. The value of the integral
where 'a' and 'b' are the statistical attributes of the random variable {x}. The value of the integral
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Type II error in hypothesis testing is
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A random variable X has a probability density function, {\text{f}}\left( {\text{x}} \right) = \left\{ {\begin{array}{*{20}{c}}
{{\text{k}}{{\text{x}}^{\text{n}}}{{\text{e}}^{ - {\text{x}}}};}&{{\text{x}} \geqslant {\text{0}}} \\
{0;}&{{\text{otherwise}}}
\end{array}} \right. (n is an integer) with mean 3. The values of {k, n} are
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A six-faced fair dice is rolled five times. The probability (in%) of obtaining "ONE" at least four times is
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A probability density function is of the form
The value of K is
The value of K is
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A box contains 20 defective items and 80 non-defective items. If two items are selected at random without replacement, what will be the probability that both items are defective?
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A class of first year B. Tech. students is composed of four batches A, B, C and D, each consisting of 30 students. It is found that the sessional marks of students in Engineering Drawing in batch Chave a mean of 6.6 and standard deviation of 2.3. The mean and standard deviation of the marks for the entire class are 5.5 and 4.2, respectively. It is
decided by the course instructor to normalize the marks of the students of all batches to have the same mean and standard deviation as that of the entire class. Due to this, the marks of a student in batch C are changed from 8.5 to
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Let X be a normal random variable with mean 1 and variance 4. The probability P{X < 0} is
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Three cards were drawn from a pack of 52 cards. The probability that they are a king, a queen, and a jack is
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A committee of 4 is to be formed from among 4 girls and 5 boys. What is the probability that the committee will have number of boys less than number of girls?
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It is estimated that average number of events during an year is three. What is the probability of occurrence of not more than two events over a two year duration? Assume that the number of events follow a Poisson's distribution.
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Suppose we uniformly and randomly select a permutation from the 20! permutations of 1, 2, 3 ...., 20. What is the probability that 2 appears at an earlier position that any other even number in the selected permutation?
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The standard normal cumulative probability function (probability from to xn) can be approximated as where xn = standard normal deviate. If mean and standard deviation of annual precipitation are 102 cm and 27 cm respectively, the probability that the annual precipitation will be between 90 cm and 102cm is
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A probability distribution with right skew is shown in the figure.
The correct statement for the probability distribution is
The correct statement for the probability distribution is
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Let X be a random variable following normal distribution with mean +1 and variance 4. Let Y be another normal variable with mean -1 and variance unknown. If P(X ≤ -1) = P(Y ≥ 2) the standard deviation of Y is
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