Advertisements
Advertisements
प्रश्न
If X has a Poisson distribution with variance 2, find
Mean of X [Use e-2 = 0.1353]
Advertisements
उत्तर
Mean = Variance = 2
∴ Mean= 2
APPEARS IN
संबंधित प्रश्न
If X has a Poisson distribution with variance 2, find P (X = 4)
[Use e-2 = 0.1353]
If X has a Poisson distribution with variance 2, find P(X ≤ 4)
[Use e-2 = 0.1353]
If X has Poisson distribution with m = 1, then find P(X ≤ 1) given e−1 = 0.3678
If X~P(0.5), then find P(X = 3) given e−0.5 = 0.6065.
The number of complaints which a bank manager receives per day follows a Poisson distribution with parameter m = 4. Find the probability that the manager receives only two complaints on a given day
The number of complaints which a bank manager receives per day follows a Poisson distribution with parameter m = 4. Find the probability that the manager receives a) only two complaints on a given day, b) at most two complaints on a given day. Use e−4 = 0.0183.
It is known that, in a certain area of a large city, the average number of rats per bungalow is five. Assuming that the number of rats follows Poisson distribution, find the probability that a randomly selected bungalow has exactly 5 rats inclusive. Given e-5 = 0.0067.
It is known that, in a certain area of a large city, the average number of rats per bungalow is five. Assuming that the number of rats follows Poisson distribution, find the probability that a randomly selected bungalow has between 5 and 7 rats inclusive. Given e−5 = 0.0067.
The expected value of the sum of two numbers obtained when two fair dice are rolled is ______.
Choose the correct alternative:
A distance random variable X is said to have the Poisson distribution with parameter m if its p.m.f. is given by P(x) = `("e"^(-"m")"m"^"x")/("x"!)` the condition for m is ______
State whether the following statement is True or False:
X is the number obtained on upper most face when a die is thrown, then E(x) = 3.5
State whether the following statement is True or False:
If n is very large and p is very small then X follows Poisson distribution with n = mp
The probability that a bomb will hit the target is 0.8. Using the following activity, find the probability that, out of 5 bombs, exactly 2 will miss the target
Solution: Let p = probability that bomb miss the target
∴ q = `square`, p = `square`, n = 5.
X ~ B`(5, square)`, P(x) = `""^"n""C"_x"P"^x"q"^("n" - x)`
P(X = 2) = `""^5"C"_2 square = square`
If X has Poisson distribution with parameter m and P(X = 2) = P(X = 3), then find P(X ≥ 2). Use e–3 = 0.0497.
P[X = x] = `square`
Since P[X = 2] = P[X = 3]
`square` = `square`
`m^2/2 = m^3/6`
∴ m = `square`
Now, P[X ≥ 2] = 1 – P[x < 2]
= 1 – {P[X = 0] + P[X = 1]
= `1 - {square/(0!) + square/(1!)}`
= 1 – e–3[1 + 3]
= 1 – `square` = `square`
