# Some questions about random variables probability

• yousif1429
In summary, the first question asks a student to find the probability of something happening over an interval, and the second asks for an approximation to the limit of this integral. The student is not able to answer the first question, but finds a solution from a book.
yousif1429
I have some questions I could not find answer I hope here to get the correct answer

my questions here in this picture ( attached ) 2 questions

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Hey yousif1429 and welcome to the forums.

It would help us if you showed your working out and also told us what you are thinking and why you are thinking that.

We can't just solve things for you on these forums per the forum rules, so to help the readers we need to know some of these details.

ok i found solutions for second question but the first one i did not found yet
the purpose of these questions because tomorrow i have quiz and my teacher bring this question in last semester and i said for my self may he will repeat it again
please if you know solve the first one please because i looked in my book similar to this question and i did not find i get tired now and my exam is tomorrow i hope some one help me .

thank you ,

yousif1429 said:
ok i found solutions for second question but the first one i did not found yet
the purpose of these questions because tomorrow i have quiz and my teacher bring this question in last semester and i said for my self may he will repeat it again
please if you know solve the first one please because i looked in my book similar to this question and i did not find i get tired now and my exam is tomorrow i hope some one help me .

thank you ,

Hint for the number 1: What is the definition of the probability over an interval for a bivariate function? What are the limits for this integral given the information in the question?

ok no thank you i found the solution from my friends

## 1. What is a random variable?

A random variable is a numerical value that is assigned to each outcome of a random event. It can take on different values with different probabilities, and is used to represent uncertainty in a mathematical way.

## 2. How is probability related to random variables?

Probability is used to describe the likelihood of different outcomes of a random variable. It assigns a value between 0 and 1 to each possible outcome, with 0 representing impossibility and 1 representing certainty.

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

Discrete random variables can only take on a finite or countably infinite number of values, while continuous random variables can take on any value within a certain range. For example, the number of heads in 10 coin tosses is a discrete random variable, while the height of a person is a continuous random variable.

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

The expected value of a random variable is calculated by multiplying each possible outcome by its respective probability and summing them all together. It represents the average value that we would expect to see if we repeated the random experiment many times.

## 5. What is the significance of the variance and standard deviation of a random variable?

The variance and standard deviation of a random variable measure the spread or variability of its values around the expected value. A smaller variance/standard deviation indicates that the values are closer to the expected value, while a larger variance/standard deviation indicates more variability.

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