Answer:
(a) P(X=1)=0.46
(b) E[X]=1.3
Step-by-step explanation:
(a)
Let A be the event that first coin will land on heads and B be the event that second coin will land on heads.
According to the given information
P(X=1) is the probability of getting exactly one head.
P(X=1) = P(1st heads and 2nd tails ∪ 1st tails and 2nd heads)
= P(1st heads and 2nd tails) + P(1st tails and 2nd heads)
Since the two events are disjoint, therefore we get
Therefore the value of P(X=1) is 0.46.
(b)
Thevalue of E[X] is
![E[X]=\sum_{x}xP(X=x)](https://tex.z-dn.net/?f=E%5BX%5D%3D%5Csum_%7Bx%7DxP%28X%3Dx%29)
![E[X]=0P(X=0)+1P(X=1)+2P(X=2)](https://tex.z-dn.net/?f=E%5BX%5D%3D0P%28X%3D0%29%2B1P%28X%3D1%29%2B2P%28X%3D2%29)
![E[X]=P(X=1)+2P(X=2)](https://tex.z-dn.net/?f=E%5BX%5D%3DP%28X%3D1%29%2B2P%28X%3D2%29)
..... (1)
First we calculate the value of P(X=2).
P{X = 2} = P(1st heads and 2nd heads)
= P(1st heads)P(2nd heads)
Substitute P(X=1)=0.46 and P(X=2)=0.42 in equation (1).
![E[X]=0.46+2(0.42)](https://tex.z-dn.net/?f=E%5BX%5D%3D0.46%2B2%280.42%29)
![E[X]=1.3](https://tex.z-dn.net/?f=E%5BX%5D%3D1.3)
Therefore the value of E[X] is 1.3.
Answer:
the slope is 3
Step-by-step explanation:
Answer:
D. There is not convincing evidence of a relationship between annual company profit and median annual salary paid by the company.
Step-by-step explanation:
In this hypothesis test, the null hypothesis usually states that there is no relationship between the two variables in study.
In opposite, the claim that is being tested is the speculative hypothesis: that there is a significant relationship between both variables.
The researcher takes a sample and the P-value indicates the probability of getting that sample by pure chance <em>if the null hypothesis is true</em>.
Then, a very small P-value, below the significance level, indicates that the sample is very unusual if the null hypothesis is true, what gives evidence to reject the null hypothesis.
In this case, a P-value of 0.56 indicates that the sample is not unusual if the null hypothesis is true, so it gives no support to the claim that the null hypothesis is false and that there exists a relationship between the two variables in study.
