1. Define Probability density and distribution function.
2. Define the expected value of Discrete Random variable and Continuous Random Variable.
3. Define skew of a Random variable.
4. Define various types of transformation of Random variables.
5. A continuous random variable X has a probability density function is given by
f(x)=3 x2 0 ≤ x ≤ 1. Find a such that P(X≤a)=P(X>a).
6. Write the expression for pdf of a Poisson and binomial Random variable.
7. Define mean and variance of a random variable.
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- Probability density function (PDF) is a statistical expression that defines a probability distribution (the likelihood of an outcome) for a discrete random variable (e.g., a stock or ETF) as opposed to a continuous random variable.
- A discrete random variable has a countable number of possible values. The probability of each value of a discrete random variable is between 0 and 1, and the sum of all the probabilities is equal to 1. A continuous random variable takes on all the values in some interval of numbers.
- In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The skewness value can be positive, zero, negative, or undefined. ... In cases where one tail is long but the other tail is fat, skewness does not obey a simple rule.
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