Engineering Mat...

In a certain factory of turning razor blades, there is a small chance (1/500) for any blade to be defective. The blades are supplied in packets of 10. Use Poisson distribution to calculate the approximate number of packets containing at least one defective blade in a consignment of 10,000 packets

Let X be a binomial random variable with mean 1 and variance \(\frac{3}{4}\). The probability that X takes the value of 3 is

Probability density function of a random variable X is given below

\(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {0.25}&{if\;1 \le x \le 5}\\ 0&{otherwise} \end{array}} \right.\)

P (X ≤ 4) is

Out of 800 families with 4 children each, how many families would be expected to have 2 boys and 2 girls.

If a random variable X has a Poisson distribution with mean 5, then the expectation E[(X + 3)2] equals ______.

At a busy traffic intersection, the probability p of an individual car having an accident is p = 0.0001. If 1000 cars pass through the intersection between 5 P.M and 6 P.M. every day, then the probability that two or more car accidents occur during that period is ______. (use Poisson distribution)

A continuous random variable  has a probability density function as

f(x) = 3x², 0 ≤ x ≤ 1, Find a and b such that

(i) P(X ≤ a) = P(X > a) and

(ii) P(X > b) = 0.05

A die is tossed 180 times. Using normal distribution find the probability that the face 4 will turn up atleast 35 times (Area under the normal curve between Z = 0 and Z = 1 is 0.3413)