# GATE Questions & Answers of Probability and Statistics Civil Engineering

#### Probability and Statistics 19 Question(s)

Probability (up to one decimal place) of consecutively picking 3 red balls without replacement from a box containing 5 red balls and 1 white ball is ______

A two-faced fair coin has its faced designated as head (H) and tail(T). This coin is tossed three times in succession to record the following outcomes. H, H, H. If the coin is tossed one more time. the probability (up to one decimal place) of obtaining H again, given the previous realizations of H, H and H would be _________

Type II error in hypothesis testing is

Probability density function of a random variable X is given below

$\mathrm{P}\left(\mathrm{X}\le 4\right)$ is

The spot speeds (expressed in km/hr) observed at a road section are 66, 62, 45, 79, 32, 51, 56, 60, 53, and 49. The median speed (expressed in km/hr) is _________

(Note: answer with one decimal accuracy)

If f(x) and g(x) are two probability density functions,

Which one  of  the following ststments is true ?

Consider the following probability mass function (p.m.f) of a random variable X.

p(x,q) =

If =0.4, the variance of X is _________.

The probability density function of a random variable, $x$ is

The mean, ${\mu }_{x}$ of the random variable is ________.

The probability density function of evaporation E on any day during a year in a watershed is given by

The probability that E lies in between 2 and 4 mm/day in a day in the watershed is (in decimal) _____________

A fair (unbiased) coin was tossed four times in succession and resulted in the following outcomes: (i) Head, (ii) Head, (iii) Head, (iv) Head. The probability of obtaining a 'Tail' when the coin is tossed again is

If {x} is a continuous, real valued random variable defined over the interval (− ∞,+ ∞) and its occurrence is defined by the density function given as: $f\left(x\right)=\frac{1}{\sqrt{2\mathrm{\pi }}*b}{e}^{\frac{1}{2}{\left(\frac{x-a}{b}\right)}^{2}}$where 'a' and 'b' are the statistical attributes of the random variable {x}. The value of the integral ${\int }_{-\infty }^{a}\frac{1}{\sqrt{2\mathrm{\pi }}*b}{e}^{\frac{1}{2}{\left(\frac{x-a}{b}\right)}^{2}}dx$ is

Find the value of λ such that the function f(x) is a valid probability density function. __________

The annual precipitation data of a city is normally distributed with mean and standard deviation as 1000 mm and 200 mm, respectively. The probability that the annual precipitation will be more than 1200 mm is

In an experiment, positive and negative values are equally likely to occur. The probability of obtaining at most one negative value in five trials is

There are two containers, with one containing 4 Red and 3 Green balls and the other containing 3Blue 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

Two coins are simultaneously tossed. The probability of two heads simultaneously appearing is

The standard normal probability function can be approximated as

$\mathrm{F}\left({x}_{\mathrm{N}}\right)=\frac{1}{1+\mathrm{exp}\left(-1.7255x{}_{\mathrm{N}}{\left|{x}_{\mathrm{N}}\right|}^{0.12}\right)}$

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 102 cm is

If probability density function of a random variable X is

f(x) = x2 for -1 ≤ x ≤ 1, and
= 0 for any other value of x

Then, the percentage probability $P\left(-\frac{1}{3}\le x\le \frac{1}{3}\right)$ is