A steel products factory has two main sections. One is in charge of the metal casting process. The other performs heat t

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A steel products factory has two main sections. One is in charge
of the metal casting process. The other performs heat treatments on
previously cast pieces. It is known that 68% of the operators
belong to the foundry section, while the remaining percentage of
operators work for the heat treatment section. According to an
occupational risk study carried out by the company, it is known
that if an operator belongs to the foundry section, he has an
accident 0, 1, 2, or 3 times in a year, with a probability of 0.65,
0.15, 0.17, and 0.03, respectively, while, if an operator works in
the heat treatment section, he has an accident 0, 1, or 2 times in
a year, with probability 0.78, 0.17 and 0.05, respectively. The
random variable 𝑿 is defined as the number of accidents an operator
has in a year.
A. Find the probability function of the random
variable X, clearly specifying its Range.
B. Find the cumulative distribution function of
the random variable X.
C. Calculate the expected value of the random
variable X and interpret its result.