## Statistics

### GATE-CH-2010-13-math-1mark

2010-13-math

The Maxwell-Boltzmann velocity distribution for the $$x$$-component of the velocity at temperature $$T$$, is $f(v_x) = \sqrt {\frac {m}{2\pi kT}}\exp \left (-\frac {mv_x^2}{2kT}\right )$ The standard deviation of the distribution is

• $$\sqrt {2kT/m}$$

• $$kT/m$$

• $$\sqrt {kT/m}$$

• $$kT/2m$$

### GATE-CH-2013-1-math-1mark

2013-1-math

The number of emails received on six consecutive days is 11, 9, 18, 18, 4 and 15, respectively. What are the median and the mode for these data?

• 18 and 11, respectively

• 13 and 18, respectively

• 13 and 12.5, respectively

• 12.5 and 18, respectively

### GATE-CH-2017-5-math-1mark

2017-5-math

The marks obtained by a set of students are: $$38, 84, 45, 70, 75, 60, 48$$. The mean and median marks, respectively, are:

• 45 and 75

• 55 and 48

• 60 and 60

• 60 and 70

### GATE-CH-2007-28-math-2mark

2007-28-math

The thickness of a conductive coating in micrometers has a probability density function of $$600x^{-2}$$ for $$100 ?\mu \text {m} < x < 120 ?\mu \text {m}$$. The mean and the variance of the coating thickness is

• 1 $$\mu$$m, 108.39 $$\mu$$m$$^2$$

• 33.83 $$\mu$$m, 1 $$\mu$$m$$^2$$

• 105 $$\mu$$m, 11 $$\mu$$m$$^2$$

• 109.39 $$\mu$$m, 33.83 $$\mu$$m$$^2$$

### GATE-CH-2008-27-math-2mark

2008-27-math

The normal distribution is given by $f(x) = \frac {1}{\sqrt {2\pi }\sigma }\exp \left (-\frac {(x-\mu )^2}{2\sigma ^2}\right ), \quad -\infty < x < \infty$ The points of inflexion to the normal curve are

• $$x=-\sigma , +\sigma$$

• $$x=\mu +\sigma , \mu -\sigma$$

• $$x=\mu +2\sigma , \mu -2\sigma$$

• $$x=\mu +3\sigma , ? \mu -3\sigma$$

[Index]

### GATE-CH-2008-30-math-2mark

2008-30-math

The Poisson distribution is given by $$\displaystyle P(r) = \frac {m^r}{r!}\exp (-m)$$. The first moment about the origin for this distribution is

• 0

• $$m$$

• $$1/m$$

• $$m^2$$

### GATE-CH-2011-29-math-2mark

2011-29-math

Fuel cell stacks are made of NINE membrane electrode assemblies (MEAs) interleaved between TEN bipolar plates (BPs) as illustrated below. The width of a membrane electrode assembly and a bipolar plate are normally distributed with $$\mu _{\text {MEA}}=0.15$$, $$\sigma _{\text {MEA}}=0.01$$, and $$\mu _{\text {BP}}=5$$, $$\sigma _{\text {BP}}=0.1$$ respectively. The widths of the different layers are independent of each other.

Which ONE of the following represents the CORRECT values of $$(\mu _{\text {stack}}, \sigma _{\text {stack}})$$ for the overall fuel cell stack width?

• $$(51.35,0.32)$$

• $$(51.35,1.09)$$

• $$(5.15,0.10)$$

• $$(5.15,0.11)$$

### GATE-CH-2014-29-math-2mark

2014-29-math

Consider the following two normal distributions

\begin{align*} f_1(x) &= \exp(-\pi x^2) \\ f_2(x) &= \frac{1}{2\pi}\exp\left\{-\frac{1}{4\pi}(x^2+2x+1)\right\} \end{align*}

If $$\mu$$ and $$\sigma$$ denote the mean and standard deviation, respectively, then

• $$\mu _1<\mu _2$$ and $$\sigma _1^2<\sigma _2^2$$

• $$\mu _1<\mu _2$$ and $$\sigma _1^2>\sigma _2^2$$

• $$\mu _1>\mu _2$$ and $$\sigma _1^2<\sigma _2^2$$

• $$\mu _1>\mu _2$$ and $$\sigma _1^2>\sigma _2^2$$

### GATE-ME-2004-31-math-2mark

ME-2004-31-math

From a pack of regular from playing cards two cards are drawn random. What is the probability that both cards will be kings, if first card is NOT replaced?

• $$\dfrac {1}{26}$$

• $$\dfrac {1}{52}$$

• $$\dfrac {1}{169}$$

• $$\dfrac {1}{221}$$

### GATE-ME-2013-A-24-math-1mark

ME-2013-A-24-math

Let $$X$$ be a normal random variable with mean 1 and variance 4. The probability $$P\{X<0\}$$ is

• 0.5

• Greater than 0 and less than 0.5

• Greater than 0.5 and less than 1.0

• 1.0

[Index]