The number of flaws in a 1-inch length of copper wire manufactured by a certain process varies from wire to wire. Overall, 48% of the wires produced have no flaws, 39% have one flaw, 12% have two flaws, and 1% have three flaws. Let ? be the number of flaws in a randomly selected piece of wire. Then ?(?=0)=0.48, ?(?=1)=0.39, ?(?=2)=0.12, ?(?=3)=0.01. Let ?(?) denote the cumulative distribution function for the random variable ? that represents the number of flaws in a randomly chosen wire. a. Find ?(2). b. Find ?(1.5). c. Determine the cumulative distribution function ?(?). Hint: your answer should be a piecewise function with the following categories: ??<0, 0≤??<1, 1≤??<2, 2≤??<3, ??≥3. d. Plot ?(?).
The number of flaws in a 1-inch length of copper wire manufactured by a certain process varies from wire to wire. Overall, 48% of the wires produced have no flaws, 39% have one flaw, 12% have two flaws, and 1% have three flaws. Let ? be the number of flaws in a randomly selected piece of wire. Then ?(?=0)=0.48, ?(?=1)=0.39, ?(?=2)=0.12, ?(?=3)=0.01. Let ?(?) denote the cumulative distribution
a. Find ?(2).
b. Find ?(1.5).
c. Determine the cumulative distribution function ?(?). Hint: your answer should be a
d. Plot ?(?).
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