The probability density function of a continuous random variable is defined as follows: f(x)=c when -1≤x≤1=0, otherwise the value of c is?

Question

Answer

Calculation of c in Probability Density Function

Given:

The probability density function of a continuous random variable is defined as follows: f(x)=c when -1≤x≤1=0, otherwise.

Calculation:

As probability density function integrates to 1, we can use this property to calculate the value of c.

∫_-∞^∞ f(x) dx = 1

∫_-1¹ c dx = 1

c [x] _-1¹ = 1

c (1-(-1)) = 1

c = 1/2

Conclusion:

The value of c is 1/2.