A discrete random variable X has this probability distribution.a) Complete the table (10 pts)Compute:b) 𝜇 = 𝐸(𝑋) = ∑[𝑥𝑃(𝑥)] = ___________________ (2 points)c) 𝑉𝑎𝑟(𝑋) = ∑[(𝑥 − 𝜇)2𝑃(𝑥)] = ___________________ (2 points)d) Standard deviation. ___________________ (1 points)Note: Answers from b – d, round off to 2 decimal places. For the table take all decimal places.𝑥 0 1 2 3 4𝑃(𝑥) 0.12 0.25 0.18 0.35 0.10𝑥𝑃(𝑥)𝑥 − 𝜇(𝑥 − 𝜇)2(𝑥 − 𝜇)2𝑃(𝑥)

Sure, let's solve this step by step.

First, we need to complete the table. We calculate 𝑥𝑃(𝑥) by multiplying each value of 𝑥 with its corresponding 𝑃(𝑥).

𝑥 0 1 2 3 4 𝑃(𝑥) 0.12 0.25 0.18 0.35 0.10 𝑥𝑃(𝑥) 0 0.25 0.36 1.05 0.40

Next, we calculate 𝜇 = 𝐸(𝑋) = ∑[𝑥𝑃(𝑥)] by adding all the values of 𝑥𝑃(𝑥) we just calculated.

𝜇 = 0 + 0.25 + 0.36 + 1.05 + 0.40 = 2.06

Now, we calculate (𝑥 − 𝜇) and (𝑥 − 𝜇)² for each 𝑥.

𝑥 0 1 2 3 4 𝑃(𝑥) 0.12 0.25 0.18 0.35 0.10 𝑥𝑃(𝑥) 0 0.25 0.36 1.05 0.40 𝑥 − 𝜇 -2.06 -1.06 -0.06 0.94 1.94 (𝑥 − 𝜇)² 4.24 1.12 0.0036 0.88 3.76

Finally, we calculate 𝑉𝑎𝑟(𝑋) = ∑[(𝑥 − 𝜇)²𝑃(𝑥)] by multiplying each (𝑥 − 𝜇)² with its corresponding 𝑃(𝑥) and adding them up.

𝑉𝑎𝑟(𝑋) = 4.240.12 + 1.120.25 + 0.00360.18 + 0.880.35 + 3.76*0.10 = 1.01

The standard deviation is the square root of the variance.

Standard deviation = √1.01 = 1.00 (rounded to 2 decimal places)

So, the answers are:

b) 𝜇 = 2.06 c) 𝑉𝑎𝑟(𝑋) = 1.01 d) Standard deviation = 1.00