Question

Problem 1. Let ( mathrm{X} ) be a discrete random variable with the following PMF [ P_{X}(x)=left{egin{array}{ll} 0.1 & ext { for } x=0.2 \ 0.2 & ext { for } x=0.4 \ 0.2 & ext { for } x=0.5 \ 0.3 & ext { for } x=0.8 \ 0.2 & ext { for } x=1 \ 0 & ext { otherwise } end{array} ight. ] a. Find ( R_{X} ), the range of the random variable ( X ). b. Find ( P(X leq 0.5) ). c. Find ( P(0.25<X<0.75) ). d. Find ( P(X=0.2 mid X<0.6) ).

          Problem 1. Let ( mathrm{X} ) be a discrete random variable with the following PMF
[
P_{X}(x)=left{egin{array}{ll}
0.1 & 	ext { for } x=0.2 \
0.2 & 	ext { for } x=0.4 \
0.2 & 	ext { for } x=0.5 \
0.3 & 	ext { for } x=0.8 \
0.2 & 	ext { for } x=1 \
0 & 	ext { otherwise }
end{array}
ight.
]
a. Find ( R_{X} ), the range of the random variable ( X ).
b. Find ( P(X leq 0.5) ).
c. Find ( P(0.25<X<0.75) ).
d. Find ( P(X=0.2 mid X<0.6) ).

Problem 1. Let ( mathrmX ) be a discrete random variable with the following PMF
[
PX(x)=lefteginarrayll
0.1 ext for x=0.2 0.2 ext for x=0.4 0.2 ext for x=0.5 0.3 ext for x=0.8 0.2 ext for x=1 0 ext otherwise
endarray
ight.
]
a. Find ( RX ), the range of the random variable ( X ).
b. Find ( P(X leq 0.5) ).
c. Find ( P(0.25<X<0.75) ).
d. Find ( P(X=0.2 mid X<0.6) ).

Added by Jessica M.

Probability with Applications in Engineering, Science, and Technology

Matthew A. Carlton • Jay L. Devore 2nd Edition

Instant Answer

Solved by Expert Jason Horton

03/18/2023

Step 1

Based on the given probability mass function (PMF), the range \(R_X\) includes all the values of \(x\) for which \(P_X(x) > 0\). Therefore, from the given PMF, we can see that: \[ R_X = \{0.2, 0.4, 0.5, 0.8, 1\} \] Show more…

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