Probability -Random variable

Thread starter karthickprem
Start date Oct 22, 2010
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Probability Variable

In summary, A random variable is a variable whose possible values are outcomes of a random phenomenon. It can be discrete or continuous, with probability used to determine the likelihood of outcomes. Real-life applications include modeling stock prices in finance. The expected value is calculated by multiplying each value by its probability and summing the products.

Oct 22, 2010

karthickprem

can someone help me to solve this question !

Suppose X1,X2...Xn are independent, identically distributed exponential random variables with mean 1/λ . Let Y=Max {X1,X2...Xn}. Using exactly one uniform (0,1) random number, describe how you would generate a single realization of Y.

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Oct 22, 2010

bpet

Hint: the method is very similar to the case for n=1.

1. What is a random variable?

A random variable is a variable whose possible values are outcomes of a random phenomenon. It is typically denoted by the letter X and can take on numerical values based on the probability of each outcome occurring.

2. What is the difference between discrete and continuous random variables?

A discrete random variable can only take on a finite or countably infinite number of values, while a continuous random variable can take on any value within a given range. For example, the number of heads in 10 coin flips is a discrete random variable, while the weight of a person is a continuous random variable.

3. How is probability related to random variables?

Probability is the measure of the likelihood of an event occurring. In the context of random variables, probability is used to determine the likelihood of a particular outcome or set of outcomes occurring. The probability of a random variable taking on a certain value is represented by its probability distribution.

4. Can you give an example of a real-life application of random variables?

One example of a real-life application of random variables is in the field of finance. Stock prices are often modeled as random variables, with their probability distributions used to make predictions about future stock prices and inform investment decisions.

5. How is the expected value of a random variable calculated?

The expected value of a random variable is calculated by multiplying each possible value of the random variable by its corresponding probability and then summing all of these products. It represents the average value that would be obtained if the random variable were to be repeatedly measured or observed over a large number of trials.