Advertisements
Advertisements
प्रश्न
Determine the binomial distribution for which the mean is 4 and variance 3. Also find P(X=15)
Advertisements
उत्तर
In a binomial distribution
Mean np = 4 → (1)
variance npq = 3 → (2)
Equation (2) ÷ Equation (1)
⇒ `"npq"/"np" = 3/4`
q = `3/4` p = `1 - "q" = 1 - 3/4`
p = `(4 - 3)/4`
∴ p = `1/4`
Substitute p = `1/4` in equation (1)
n = `(1/4)` = 4
n = 4 × 4
⇒ n = 16
The binomial distribution is p(X = x)ncxpxqn-x
P(X = x) = `(16/x)(1/4)^x(3/4)^(16 - x)`
P(X = 15) = `16"c"_15 (1/4)^15 (13/4)^(16 - 15)`
= `16"c"_1 (1/4)^15 (3/4)^1`
= `16 xx 1/4^15 xx 3/4`
= `(16 xx 3)/4^16`
- `(16 xx 3)/(4^2 xx 4^14)`
= `(16 xx 3)/(16 xx 4^14)`
P(X = 15) = `3/4^14`
APPEARS IN
संबंधित प्रश्न
Define Binomial distribution
If 5% of the items produced turn out to be defective, then find out the probability that out of 20 items selected at random there are exactly three defectives
In a particular university 40% of the students are having newspaper reading habit. Nine university students are selected to find their views on reading habit. Find the probability that none of those selected have newspaper reading habit
Write any 2 examples for Poisson distribution
Derive the mean and variance of poisson distribution
Choose the correct alternative:
The parameters of the normal distribution f(x) = `(1/sqrt(72pi))"e"^(-(x - 10)^2)/72 - oo < x < oo`
Choose the correct alternative:
Let z be a standard normal variable. If the area to the right of z is 0.8413, then the value of z must be:
Vehicles pass through a junction on a busy road at an average rate of 300 per hour. What is the expected number passing in two minutes?
X is a normally distributed variable with mean µ = 30 and standard deviation σ = 4. Find P(X < 40)
People’s monthly electric bills in Chennai are normally distributed with a mean of ₹ 225 and a standard deviation of ₹ 55. Those people spend a lot of time online. In a group of 500 customers, how many would we expect to have a bill that is ₹ 100 or less?
