Random variable probability problem

In summary, G(y), the cumulative distribution function of Y, is a function that gives the probability that Y is smaller than y. It is defined by integrating the probability density function of X, which is 1/4 for -1<x<3 and 0 otherwise, from -sqrt(y) to sqrt(y) for 0<=y<=9. The domain of G(y) is divided into three cases: 0 for y<0, the integration from -sqrt(y) to sqrt(y) for 0<=y<=9, and 1 for y>9.
  • #1
thereddevils
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0

Homework Statement



Continuous random variable X has probability density function defined as

f(x)= 1/4 , -1<x<3

=0 , otherwise

Continuous random variable Y is defined by Y=X^2

Find G(y), the cummulative distribution function of Y

Homework Equations





The Attempt at a Solution



G(y) = P(-sqrt(y)<=X<=sqrt(y))

What does this mean? G(Y) is defined as P(-sqrt(y)<=X<=sqrt(y)) for 0<=X<=9 ?
 
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  • #2


G(y), the cummulative probability distribution function of Y, is a function that gives the probability that Y is smaller than y.

P(-sqrt(Y)<=X<=sqrt(Y)) is a way of writing: Probability that X is in between plus and minus the square root of Y (note the use of capital Y here, y and Y are not the same thing).
 
  • #3


gerben said:
G(y), the cummulative probability distribution function of Y, is a function that gives the probability that Y is smaller than y.

P(-sqrt(Y)<=X<=sqrt(Y)) is a way of writing: Probability that X is in between plus and minus the square root of Y (note the use of capital Y here, y and Y are not the same thing).

Thanks Gerben, the next step will be to integrate the pdf?

ie [tex]G(y)=\int^{\sqrt{y}}_{-\sqrt{y}}\frac{1}{4}dx[/tex] for [tex]0\leq y\leq 9 [/tex]

?
 
  • #4


yes exactly
 
  • #5


gerben said:
yes exactly

There will be 3 cases here,

case 1 : G(y)=0 for y<0

case 2 : G(y)= integration from -sqrt(y) to sqrt(y) 1/4 dx for 0<=y<=9

case 3: G(y)=1, for y>9

Is this the domain? I doubt my domain for case 2 is correct.
 

What is a random variable?

A random variable is a variable that takes on different values based on the outcome of a random event. It is often represented by the letter X and can be either discrete (taking on a countable number of values) or continuous (taking on any value within a range).

What is a probability problem?

A probability problem is a mathematical question that involves calculating the likelihood of a certain event occurring. This is typically done using the principles of probability, which involve analyzing the possible outcomes and their corresponding probabilities.

How do you calculate the probability of a random variable?

The probability of a random variable is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This is known as the probability mass function for discrete random variables and the probability density function for continuous random variables.

What is the difference between a discrete and continuous random variable?

A discrete random variable can only take on a countable number of values, while a continuous random variable can take on any value within a range. This means that the probability of a specific value occurring for a continuous random variable is always 0, while for a discrete random variable it is a non-zero value.

Can you give an example of a random variable probability problem?

One example of a random variable probability problem is flipping a coin and calculating the probability of getting heads. The random variable in this case is the outcome of the coin flip (either heads or tails), and the probability can be calculated by dividing the number of possible outcomes (2) by the total number of outcomes (2) to get a probability of 0.5.

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