A continuous random variable X has a probability density function

f(x) = e^(-x) , 0 < x< ∞

Then P{X > 1} is

0.368
0.5
0.632
1.0
Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.33
The random variable X has a probability distribution P(X) of the following form where k is a scalar and

then value of P(X < 2) = ______

5/6
3/4
1
1/2
Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.33
The PDF (Probability Density Function) of a random variable X is given by:

where K is a constant. If a = -1 and b = 2, then P(|X| ≤ c) for c = 1/2 is

0.86
1/2
0.75
1/3
Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.33
Let X and Y be two exponentially distributed and independent random variables with mean α and β, respectively. If Z = min(X,Y), then the mean of Z is given by
min(α, β)
α + β
Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.33
If P (1) = P (5) in Poisson's distribution, find the value of mean
3.38
5.38
3.31
None of the above
Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.33
Let X be a normal random variable with mean zero and variance 9.

If a = P(X ≥ 3), then P(|X| ≤ 3) equals.

a + 1
1-2a
a - 1
a/2
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.66
The speeds of cars are measured using a radar unit, on a motorway. The speeds are normally distributed with a mean of 90 km/hr and a standard deviation of 10 km/hr. What is the probability that a car selected at chance is moving at more than 100 km/hr? (Round of upto 2 decimals)
0.15
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00
A continuous random variable X has the distribution function

F(x) = 0 if x < 1

= k (x - 1)4 if 1 < x < 3

= 1 if x > 3

The value of k is (Round of upto 2 decimals)

0.06
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00
X is a uniformly distributed random variable that takes value between 0 and 1. The value of E(X3) will be (Round of upto 2 decimals)

0.25
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00
If 3% of electronic units manufactured by a company are defective. Find the probability that in a sample of 200 units, less than 2 bulbs are defective. (Round of upto 3 decimals)
0.017
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00
The thickness x of a protective coating applied to a conductor designed to work in corrosive conditions follows a uniform distribution over the interval [20, 40] microns. Choose the correct option(s).
E(X) = 10 μm
σ (X) = 6.77 μm
Probability that the coating is less than 35 microns thick is 0.75
All options are correct
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00

Packages have a nominal net weight of 1 kg. However their actual net weights have a uniform distribution over the interval 980 g to 1030 g. Based on information, choose the correct option(s).

P(Net Weight < 1 kg) = 0.4

w: 980 < w < 1030 then P(Net Weight < w kg) = (w-980)/50

Either A or B correct

Both A and B correct

Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00
A random variable X is binomially distributed with mean 6 and variance 4.2. Find PX ≤ 6). (Round of upto 3 decimals)
0.608
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00
A manufacturer produces light-bulbs that are packed into boxes of 100. If quality control studies indicate that 0.5% of the light-bulbs produced are defective, choose the correct option(s).
Percentage of non-defective boxes is ~ 61%
P(box contain 2 or more defective) = 0.06 (round to two decimal places)
P(box contain 1 defective) = 0.30 (round to two decimal places)
None of the above are correct
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00
Suppose vehicles arrive at a signalised road intersection at an average rate of 360 per hour and the cycle of the traffic lights is set at 40 seconds. In what percentage of cycles will the number of vehicles arriving be (a) exactly 5, (b) less than 5? If, after the lights change to green, there is time to clear only 5 vehicles before the signal changes to red again, what is the probability that waiting vehicles are not cleared in one cycle? Give answer round to two decimal places. (Round of upto 2 decimals)
((0.21,0.22))
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00