Question

As a measure of intelligence, mice are timed when going through a maze to reach a reward of food. The time (in seconds) required for any mouse is a random variable Y with a density function given by f(y) = b y2 , y ≥ b, 0, elsewhere, where b is the minimum possible time needed to traverse the maze. (a) Show that f(y) has the properties of a density function

Answer 1

Using the properties of densit function,

we get that f(y) has satisfied property of a density function. So, it a density function.

A probability density function, or density function, returns the value of a function at a given value of x.

The probability density function must satisfy two requirements:

• f(x) must be non-negative for all values of the random variable.
• Integral of all values of random variable must equal 1.

We have given that, Y is a random variable and

b f(y) = by² , y>b

where , b --> the minimum possible time needed to traverse the maze.

we have check that f(y) is Probability density function or not . For this check above two requirements ,

(i) f(y) ≥ 0 for all y > 0

so, it's satisfied

(ii) Integral over all values of the random variable ₓ∫ⁿ f(y)dy = ₓ∫ⁿ(b/y²)dy where n=∞ and x = b

= ₓ[ -b/y]ⁿ

= -(0-1) = 1

Hence , f(y) is density function.

To learn more about Density function, refer:

https://brainly.com/question/20815791

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