SOCR EduMaterials Activities Discrete Probability examples
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*<math> X \sim b(8,0.3) </math>, <math> P(X=3)= {8 \choose 3} 0.3^30.7^5</math> | *<math> X \sim b(8,0.3) </math>, <math> P(X=3)= {8 \choose 3} 0.3^30.7^5</math> | ||
*<math> P(X \ge 1)=1-P(X=0)=1-.7^8 </math> | *<math> P(X \ge 1)=1-P(X=0)=1-.7^8 </math> | ||
- | *<math> E(X)= np = 8*.3=2.4 </math> | + | *<math> E(X),</math>= <math>np</math> = <math>8*.3=2.4 </math> |
*<math> Sd(X)= sqrt(npq)</math> | *<math> Sd(X)= sqrt(npq)</math> | ||
* '''Example 2:''' | * '''Example 2:''' | ||
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<math> 1/0.30 | <math> 1/0.30 | ||
</math> | </math> | ||
+ | |||
+ | * '''Example 6:''' | ||
+ | **a. <math>X \sim b(5,0.90) </math>, <math> P(X=4)= {5 \choose 4} 0.9^4 0.1^1</math> | ||
+ | **<math>P(X\ge 1)= 1-P(X=0)= 1- 0.1^4 </math> | ||
+ | **b. <math>X \sim b(4,0.8) </math>, <math> P(X=2)= {4 \choose 2} 0.8^2 0.2^2</math> |
Revision as of 21:27, 23 April 2007
- Description: You can access the applets for the above distributions at http://www.socr.ucla.edu/htmls/SOCR_Distributions.html .
- Example 1:
Find the probability that 3 out of 8 plants will survive a frost, given that any such plant will survive a frost with ptobability of 0.30. Also, find the probability that at least 1 out of 8 will survive a frost. What is the expected value and standard deviation of the number of plants that survive the frost?
- Answer:
- ,
- E(X),= np = 8 * .3 = 2.4
- Sd(X) = sqrt(npq)
- Example 2:
If the probabilities of having a male or female offspring are both 0.50, find the probability that a familiy's fifth child is their first son.
- Answer:
- 0.505
- Example 3:
- a. ,
- b. ++
- Example 4:
- 0.740.3
- Example 5:
1 / 0.30
- Example 6:
- a. ,
- b. ,