Question

If the probability density function of a random variable is given by: (f(x) = egin{cases} x & ext{for } 0 < x < 1\ 2 - x & ext{for } 1 le x < 2 end{cases}) and zero everywhere else. a) Graph the pdf. b) Verify by integration that $int_{-infty}^{infty} f(x) , dx = 1$ c) Find the probability that a random variable having this probability density will take on a value: egin{itemize} item between 0.2 and 0.8 item between 0.6 and 1.2 end{itemize} Create a new sketch of the pdf for each probability, and shade the corresponding area represented.

          If the probability density function of a random variable is given by:
(f(x) = egin{cases} x & 	ext{for } 0 < x < 1\ 2 - x & 	ext{for } 1 le x < 2 end{cases})
and zero everywhere else.
a) Graph the pdf.
b) Verify by integration that $int_{-infty}^{infty} f(x) , dx = 1$
c) Find the probability that a random variable having this probability density will take on a
value:
egin{itemize}
    item between 0.2 and 0.8
    item between 0.6 and 1.2
end{itemize}
Create a new sketch of the pdf for each probability, and shade the corresponding area
represented.

If the probability density function of a random variable is given by:
(f(x) = egincases x extfor 0 < x < 1 2 - x extfor 1 le x < 2 endcases)
and zero everywhere else.
a) Graph the pdf.
b) Verify by integration that int-infty^infty f(x) , dx = 1
c) Find the probability that a random variable having this probability density will take on a
value:
eginitemize
item between 0.2 and 0.8
item between 0.6 and 1.2
enditemize
Create a new sketch of the pdf for each probability, and shade the corresponding area
represented.

Added by Ashley H.

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