∫ x e

∫ x e − | | is an even function) > = ( ) − ∞ Γ Γ Γ ( ) ∵ ( ) ; )! α α α (n) V X E X E X  = − [ ] Exercise . . Find the expected value for the random variable of an unbiased die .

Let X be a random variable defining number of students getting A grade. Find the expected value of X from the given table X = x P ( X = x ) . . .

. . The following table is describing about the probability mass function of the random variable X P ( x ) . .

. Find the standard deviation of x . . Let X be a continuous random variable with probability density function f otherwise X ( ) = ≤≤    Find the expected value of X .

. Let X be a continuous random variable with probability density function otherwise ( ) = ≥      , Find the mean and variance of X . . In an investment, a man can make a profit of ` , with a probability of .

or XII Std - Business Maths & Stat EM Chapter - - Random Variable and Mathematical Expectation a loss of ` , with a probability of ⋅ Find the expected gain. . What are the properties of Mathematical expectation? .

What do you understand by Mathematical expectation? . How do you define variance in terms of Mathematical expectation? .

Define Mathematical expectation in terms of discrete random variable. . State the definition of Mathematical expectation using continuous random variable. .

In a business venture a man can make a profit of ` , with a probability of . or have a loss of ` , with a probability of ⋅ . What is his expected, variance and standard deviation of profit? .

The number of miles an automobile tire lasts before it reaches a critical point in tread wear can be represented