Financial Risk Manager Part 1

Step 1: Find the value of C

The sum of all probabilities must equal 1:

$C = 1 - 0.15 - 0.25 - 0.35 = 0.25$

Step 2: Determine the probabilities for each value

• $P(X=1) = 0.15$
• $P(X=2) = 0.25$
• $P(X=3) = 0.35$
• $P(X=4) = 0.25$

Step 3: Identify the mode

The mode is the value with the highest probability. Comparing the probabilities:

• $P(X=1) = 0.15$
• $P(X=2) = 0.25$
• $P(X=3) = 0.35$ (highest)
• $P(X=4) = 0.25$

The value $x=3$ has the highest probability of 0.35.

Step 4: Conclusion

The mode of the distribution is $x=3$, which corresponds to option D (3.0).