Normal Distribution properties
Trending Questions
Q.
The area (in percentage) under standard normal distribution curve of random variable Z within limits from -3 to +3 is _____.
- 99.7
Q. If f(x) is a continous real valued random variable defined over the interval (−∞, +∞) and its occurance is defined by the density function given as f(x)=1√2πbexp{−12(x−ab)2} where a and b are the statistical attributes of the random variable {x}. The value of the integral ∫a−∞1√2πbexp{−12(x−ab)2}dx is
- 1
- 0.5
- π
- π/2
Q. Number of tigers in a reserve is normally distributed with mean and variance respectively as 1200 and 9×104. The probability of finding more than 1800 tigers is approximately.
- 0.0125
- 0.025
- 0.05
- None of these
Q.
Let X1, X2 and X3 be independent and identically distributed random variables with the uniform distribution on [0, 1]. The probability P(X1+X2≤X3) is the largest} is
- 0.16
Q. The value of 1√2π∫∞0 exp(−x28)dx is.
- 1
Q. Let U and V be two independent zero mean Gaussian random variables of variances 14 and 19 respectively. The probability P(3V≥2U) is
- 49
- 12
- 23
- 59
Q. Let X be a normal random variable with mean 1 and variance 4. The probability P(X < 0) is
- 0.5
- greater than zero and less than 0.5
- greater than 0.5 and less than 1.0
- 1.0
Q. A normal random variable X has the following probability density function
fx(x)=1√8πe−⎧⎪ ⎪⎨⎪ ⎪⎩(x−1)28⎫⎪ ⎪⎬⎪ ⎪⎭, −∞<x<∞
Then ∫∞1fx(x)dx?
fx(x)=1√8πe−⎧⎪ ⎪⎨⎪ ⎪⎩(x−1)28⎫⎪ ⎪⎬⎪ ⎪⎭, −∞<x<∞
Then ∫∞1fx(x)dx?
- 0
- 12
- 1−1e
- 1
Q. A simple random sample of 100 observations was taken from a large population. The sample mean & the standard deviation were determined to be 80 and 12 respectively. The standards error of mean is
- 1.2
Q. Consider a Gaussian distributed random variable with zero mean and standard deviation σ. The value of its cumulative distribution function at the origin will be
- 0
- 0.5
- 1
- 10σ