Exams › GATE › Engineering Mathematics

A continuous random variable X has a probability density function f(x) = e^(−x), 0 ≤ x < ∞. Then P{X > 1} is

1. 0.368
2. 0.5
3. 0.632
4. 1.0

Correct answer: 0.368

Solution

For the exponential density f(x)=e^{-x}, P(X>1)=integral from 1 to infinity of e^{-x} dx = e^{-1} = 0.368. (0.632 is P(X<1).)

Related GATE Engineering Mathematics questions

• Organic fraction of municipal solid waste (OFMSW) with bulk density of 315 kg/m³ and water content of 30% is mixed with municipal sludge of bulk density 700 kg/m³ and water content of 70%, such that the water content of the mixture is 40%. The amount (in kg) of sludge to be mixed per kg of OFMSW (rounded off to 2 decimal places) and the density of the mixture (in kg/m³) (rounded off to the nearest integer) are calculated. Which of the following options is/are true:
• A probability distribution with right skew is shown in the figure. The correct statement for the probability distribution is
• The probability density function of a continuous random variable distributed uniformly between x and y (for y > x) is
• The dimension of dynamic viscosity is:
• A single-lane highway has a traffic density of 40 vehicles/km. If the time-mean speed and space-mean speed are 40 kmph and 30 kmph, respectively, the average headway (in seconds) between the vehicles is
• A fair (unbiased) coin was tossed four times in succession and resulted in the following outcomes: (i) H head, (ii) H head, (iii) H head, (iv) H head. The probability of obtaining a 'Tail' when the coin is tossed again is

⚔️ Practice GATE Engineering Mathematics free + battle 1v1 →