Hi Saideep P(x | Y=1) and P(x | Y=2) is the conditional probability of X given Y has occurred. To calculate expected value of X - 1st Case (Y=1) = (0.2 x 0.3 x 0) + (0.4 x 0.3 x 5) + (0.4 x 0.3 x 10) = 1.8 Which means: The probability of (Y = 1) occurring is 0.3 or 30%. If Y occurs, probability ofRead more
Hi Saideep
P(x | Y=1) and P(x | Y=2) is the conditional probability of X given Y has occurred. To calculate expected value of X –
1st Case (Y=1) = (0.2 x 0.3 x 0) + (0.4 x 0.3 x 5) + (0.4 x 0.3 x 10) = 1.8
Which means: The probability of (Y = 1) occurring is 0.3 or 30%. If Y occurs, probability of X being 0 is 0.2 So, joint probability X=0 is 0.2 x 0.3 x 0. (1st bracket above) and same for the 2nd and 3rd bracket.
Similarly,
2nd Case (Y=2) = (0.1 x 0.7 x 0) + (0.8 x 0.7 x 5) + (0.1 x 0.7 x 10) = 3.5
Expected Value of X = 1.8 + 3.5 = 5.3
This is my understanding, please confirm me whether the answer is correct 🙂
Hello Archana, The confidence interval of the T/Z curve represents probability (shaded area under the curve). If the confidence interval expands i.e the gap (standard error x Z/T) increases then the probability of point interval falling in the shaded area increases as confidence interval is bigger,Read more
Hello Archana,
The confidence interval of the T/Z curve represents probability (shaded area under the curve). If the confidence interval expands i.e the gap (standard error x Z/T) increases then the probability of point interval falling in the shaded area increases as confidence interval is bigger, our value range is also bigger [mean +- z(sd)].
For eg. (Two tailed test)
1st Case: If we take Z = 1.96, area under the confidence interval i.e probability is 95% (shaded area).
2nd Case: if Z = 2.33, shaded area i.e confidence interval is 98%. As Z is more in the 2nd case, our value range [mean +- z(sd)] is bigger.
Now, we are 98% confident that our point estimate lies in the value range unlike 95% in the 1st case.
Probability concepts
Hi Saideep P(x | Y=1) and P(x | Y=2) is the conditional probability of X given Y has occurred. To calculate expected value of X - 1st Case (Y=1) = (0.2 x 0.3 x 0) + (0.4 x 0.3 x 5) + (0.4 x 0.3 x 10) = 1.8 Which means: The probability of (Y = 1) occurring is 0.3 or 30%. If Y occurs, probability ofRead more
Hi Saideep
P(x | Y=1) and P(x | Y=2) is the conditional probability of X given Y has occurred. To calculate expected value of X –
1st Case (Y=1) = (0.2 x 0.3 x 0) + (0.4 x 0.3 x 5) + (0.4 x 0.3 x 10) = 1.8
Which means: The probability of (Y = 1) occurring is 0.3 or 30%. If Y occurs, probability of X being 0 is 0.2 So, joint probability X=0 is 0.2 x 0.3 x 0. (1st bracket above) and same for the 2nd and 3rd bracket.
Similarly,
2nd Case (Y=2) = (0.1 x 0.7 x 0) + (0.8 x 0.7 x 5) + (0.1 x 0.7 x 10) = 3.5
Expected Value of X = 1.8 + 3.5 = 5.3
This is my understanding, please confirm me whether the answer is correct 🙂
See lessSampling And Estimation
Hello Archana, The confidence interval of the T/Z curve represents probability (shaded area under the curve). If the confidence interval expands i.e the gap (standard error x Z/T) increases then the probability of point interval falling in the shaded area increases as confidence interval is bigger,Read more
Hello Archana,
The confidence interval of the T/Z curve represents probability (shaded area under the curve). If the confidence interval expands i.e the gap (standard error x Z/T) increases then the probability of point interval falling in the shaded area increases as confidence interval is bigger, our value range is also bigger [mean +- z(sd)].
For eg. (Two tailed test)
1st Case: If we take Z = 1.96, area under the confidence interval i.e probability is 95% (shaded area).
2nd Case: if Z = 2.33, shaded area i.e confidence interval is 98%. As Z is more in the 2nd case, our value range [mean +- z(sd)] is bigger.
Now, we are 98% confident that our point estimate lies in the value range unlike 95% in the 1st case.
See less