density function question, please help

[jamest96]

I'm stuck on parts B and C of this question, can anybody help please:

3. a) Show that the following represents a density function:

. . . . .\(\displaystyle f(x)\, =\, 3x^2\, \mbox{ for }\, 0\, <\, x\, <\, 1\)

b) Sketch a graph of this function and indicate the area associated with the probability that \(\displaystyle \,0.1\, <\, x\, <\, 0.5.\)

c) Calculate the probability that \(\displaystyle \,0.1\, <\, x\, <\, 0.5.\)

any help would be really appreciated, thanks,
Jamest96

 

[pka]

I'm stuck on parts B and C of this question, can anybody help please:

3. a) Show that the following represents a density function:

. . . . .\(\displaystyle f(x)\, =\, 3x^2\, \mbox{ for }\, 0\, <\, x\, <\, 1\)

b) Sketch a graph of this function and indicate the area associated with the probability that \(\displaystyle \,0.1\, <\, x\, <\, 0.5.\)

c) Calculate the probability that \(\displaystyle \,0.1\, <\, x\, <\, 0.5.\)

any help would be really appreciated, thanks,
Jamest96

a) Is \(\displaystyle f(x)\ge 0~?\) and \(\displaystyle \int_0^1 {f(x)dx} =1~ ?\)

c) What does \(\displaystyle \int_{0.1}^{0.5} {f(x)dx} = ?\)

 

[jamest96]

a) Is \(\displaystyle f(x)\ge 0~?\) and \(\displaystyle \int_0^1 {f(x)dx} =1~ ?\)

c) What does \(\displaystyle \int_{0.1}^{0.5} {f(x)dx} = ?\)

Thanks I understand it now