Probability and Stat

5. 𝐸 𝑋 = Σ𝑥(𝑃 𝑥 ) 𝜇 = Σ𝑥(𝑃 𝑥 )
(1)(1/6) (2)(1/6) (3)(1/6) (4)(1/6) (5)(1/6) (6)(1/6)
1/6 2/6 3/6 4/6 5/6 6/6
+ + + + +
𝐸 𝑋 = 21/6 𝑜𝑟 3.5

6. 𝐸 𝑋 = Σ𝑥(𝑃 𝑥 ) 𝜇 = Σ𝑥(𝑃 𝑥 )
= −2 0.42 + −1 0.15 + 0 0.16 + 1 0.17 + (2)(0.10)
= (-0.84)+ (-0.15)+ (0)+ (0.17)+
𝐸 𝑋 = −0.62
A random variable X has a probability distribution as shown in
the table. Find the mean or expected value of x or E(X).
(0.20)

7. 𝝈𝟐
𝜎2
𝝈𝟐
= 𝜮 𝒙 − 𝝁 𝟐
𝑷(𝑿)
𝝈𝟐 = 𝝈

8. 𝐸 𝑋 = Σ𝑥(𝑃 𝑥 ) 𝜇 = Σ𝑥(𝑃 𝑥 )
(1)(1/6) (2)(1/6) (3)(1/6) (4)(1/6) (5)(1/6) (6)(1/6)
1/6 2/6 3/6 4/6 5/6 6/6
+ + + + +
𝐸 𝑋 = 21/6 𝑜𝑟 3.5

9. 𝜇 = 3.5
𝐸 𝑋 = 3.5
𝝈𝟐
= 𝜮 𝒙 − 𝝁 𝟐
𝑷(𝑿)
𝟏 − 𝟑. 𝟓 𝟐
(
𝟏
𝟔
) 𝟐 − 𝟑. 𝟓 𝟐
(
𝟏
𝟔
) 𝟑 − 𝟑. 𝟓 𝟐
(
𝟏
𝟔
) 𝟒 − 𝟑. 𝟓 𝟐
(
𝟏
𝟔
) 𝟓 − 𝟑. 𝟓 𝟐
(
𝟏
𝟔
) 𝟔 − 𝟑. 𝟓 𝟐
(
𝟏
𝟔
)
𝟏. 𝟎𝟒𝟐 𝟎. 𝟑𝟕𝟓 𝟎. 𝟎𝟒𝟐 𝟎. 𝟎𝟒𝟐 𝟎. 𝟎𝟑𝟕𝟓 𝟏. 𝟎𝟒𝟐
+ + + + +
𝝈𝟐
= 𝟐. 𝟗𝟏𝟖
𝝈𝟐 = 𝟐. 𝟗𝟏𝟖 𝝈 = 𝟏. 𝟕𝟏

10. 𝐸 𝑋 = Σ𝑥(𝑃 𝑥 ) 𝜇 = Σ𝑥(𝑃 𝑥 )
= −2 0.42 + −1 0.15 + 0 0.16 + 1 0.17 + (2)(0.10)
= (-0.84)+ (-0.15)+ (0)+ (0.17)+
𝐸 𝑋 = −0.62
A random variable X has a probability distribution as shown in
the table. Find the mean or expected value of x or E(X).
(0.20

11. 𝜇 = −0.62
A random variable X has a probability distribution as shown in the table. Find
the variance and standard deviation of x.
𝝈𝟐
= 𝜮 𝒙 − 𝝁 𝟐
𝑷(𝑿)
−𝟐 − (𝟎. 𝟔𝟐 𝟐
(𝟎. 𝟒𝟐)
𝟎. 𝟖 𝟎. 𝟎𝟐𝟐 𝟎. 𝟎𝟔𝟐 𝟎. 𝟒𝟒𝟔 𝟎. 𝟔𝟖𝟔
+ + + +
𝝈𝟐
= 𝟐. 𝟎𝟏𝟔 𝝈𝟐 = 𝟐. 𝟎𝟏𝟔 𝝈 = 𝟏. 𝟒𝟐
−𝟏 − (𝟎. 𝟔𝟐 𝟐
(𝟎. 𝟏𝟓) 𝟎 − (𝟎. 𝟔𝟐 𝟐
(𝟎. 𝟏𝟔)
𝟏 − (𝟎. 𝟔𝟐 𝟐
(𝟎. 𝟏𝟕) 𝟐 − (𝟎. 𝟔𝟐 𝟐
(𝟎. 𝟏𝟎)

12. The Ads Standard Council of the Philippines determined the number of times
buyers of a product had watched an advertisement in social media before
purchasing the product. The results are shown below:
𝜇 = Σ𝑥(𝑃 𝑥 )
(1)(0.26) (2)(0.28) (3)(0.19) (4)(0.15) (5)(0.12)
0.26 0.56 0.57 0.6 0.6
+ + + +
+
𝜇 =
𝜇 = + + +
𝜇 = 2.59
𝑇ℎ𝑒 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑖𝑚𝑒𝑠 𝑎 𝑏𝑢𝑦𝑒𝑟 𝑣𝑖𝑒𝑤𝑠 𝑡ℎ𝑒 𝑎𝑑𝑣𝑒𝑟𝑡𝑖𝑠𝑒𝑚𝑒𝑛𝑡 𝑖𝑛 𝑠𝑜𝑐𝑖𝑎𝑙
𝑚𝑒𝑑𝑖𝑎 𝑏𝑒𝑓𝑜𝑟𝑒 𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒 𝑖𝑠 2.59 𝑡𝑖𝑚𝑒𝑠.

13. The Ads Standard Council of the Philippines determined the number of times buyers of a product
had watched an advertisement in social media before purchasing the product. The results are
shown below:
𝜇 = 2.59
𝝈𝟐
= 𝜮 𝒙 − 𝝁 𝟐
𝑷(𝑿)
𝟏 − 𝟐. 𝟓𝟗 𝟐
(𝟎. 𝟐𝟔)
𝟎. 𝟔𝟓𝟕 𝟎. 𝟎𝟗𝟕 𝟎. 𝟎𝟑𝟐 𝟎. 𝟐𝟗𝟖 𝟎. 𝟔𝟗𝟕
+ + + +
𝝈𝟐
= 𝟏. 𝟕𝟖𝟏 𝝈𝟐 = 𝟏. 𝟕𝟖𝟏 𝝈 = 𝟏. 𝟑𝟑
𝟐 − 𝟐. 𝟓𝟗 𝟐
(𝟎. 𝟐𝟖) 𝟑 − 𝟐. 𝟓𝟗 𝟐
(𝟎. 𝟏𝟗)
𝟒 − 𝟐. 𝟓𝟗 𝟐
(𝟎. 𝟏𝟓) 𝟓 − 𝟐. 𝟓𝟗 𝟐
(𝟎. 𝟏𝟐)

17. 4.
5.