Step 1: List all values and probabilities We have X taking the values 2,3,5,7, and 12 . Their probabilities are 3k,k,k,2k, and k. Step 2: Make a table with useful information
xi
pi
pixi
xi2
pixi2
2
3k
6k
4
12k
3
k
3k
9
9k
5
k
5k
25
25k
7
2k
14k
49
98k
12
k
12k
144
144k
40k
288k
Step 3: Find value of k Add up all probabilities: 3k+k+k+2k+k=8k Set equal to 1 : 8k=1 So, k=‌
1
8
Step 4: Find the mean and expected value of x2 ∑pixi=40k ∑pixi2=288k Step 5: Write the formula for standard deviation SD=√∑pixi2−(∑pixi)2
Step 6: Substitute the values and solve SD=√288k−(40k)2=√‌
