Answer:
Mean = 1.42
Variance = 0.58
Step-by-step explanation:
Given: X denote the number of luxury cars sold in a given day, and Y denote the number of extended warranties sold.
Also, joint probability function of X and Y are given.
To find:
mean and variance of X
Solution:
From the given joint probability function of X and Y,
![P(X=0)=\frac{1}{6}\\P(X=1)=\frac{1}{12}+\frac{1}{6}=\frac{1+2}{12}=\frac{3}{12}\\P(X=2)=\frac{1}{12}+\frac{1}{3}+\frac{1}{6}=\frac{1+4+2}{12}=\frac{7}{12}](https://tex.z-dn.net/?f=P%28X%3D0%29%3D%5Cfrac%7B1%7D%7B6%7D%5C%5CP%28X%3D1%29%3D%5Cfrac%7B1%7D%7B12%7D%2B%5Cfrac%7B1%7D%7B6%7D%3D%5Cfrac%7B1%2B2%7D%7B12%7D%3D%5Cfrac%7B3%7D%7B12%7D%5C%5CP%28X%3D2%29%3D%5Cfrac%7B1%7D%7B12%7D%2B%5Cfrac%7B1%7D%7B3%7D%2B%5Cfrac%7B1%7D%7B6%7D%3D%5Cfrac%7B1%2B4%2B2%7D%7B12%7D%3D%5Cfrac%7B7%7D%7B12%7D)
Mean of X:
![E(X)=\sum XP(X)\\=0\left ( \frac{1}{6} \right )+1\left ( \frac{3}{12} \right )+2\left ( \frac{7}{12} \right )\\=0+\frac{3}{12}+\frac{14}{12}\\=\frac{17}{12}=1.42](https://tex.z-dn.net/?f=E%28X%29%3D%5Csum%20XP%28X%29%5C%5C%3D0%5Cleft%20%28%20%5Cfrac%7B1%7D%7B6%7D%20%5Cright%20%29%2B1%5Cleft%20%28%20%5Cfrac%7B3%7D%7B12%7D%20%5Cright%20%29%2B2%5Cleft%20%28%20%5Cfrac%7B7%7D%7B12%7D%20%5Cright%20%29%5C%5C%3D0%2B%5Cfrac%7B3%7D%7B12%7D%2B%5Cfrac%7B14%7D%7B12%7D%5C%5C%3D%5Cfrac%7B17%7D%7B12%7D%3D1.42)
Variance of X:
![E(X^2)=\sum X^2P(X)\\=0^2\left ( \frac{1}{6} \right )+1^2\left ( \frac{3}{12} \right )+2^2\left ( \frac{7}{12} \right )\\=0+\frac{3}{12}+\frac{28}{12}\\=\frac{31}{12}](https://tex.z-dn.net/?f=E%28X%5E2%29%3D%5Csum%20X%5E2P%28X%29%5C%5C%3D0%5E2%5Cleft%20%28%20%5Cfrac%7B1%7D%7B6%7D%20%5Cright%20%29%2B1%5E2%5Cleft%20%28%20%5Cfrac%7B3%7D%7B12%7D%20%5Cright%20%29%2B2%5E2%5Cleft%20%28%20%5Cfrac%7B7%7D%7B12%7D%20%5Cright%20%29%5C%5C%3D0%2B%5Cfrac%7B3%7D%7B12%7D%2B%5Cfrac%7B28%7D%7B12%7D%5C%5C%3D%5Cfrac%7B31%7D%7B12%7D)
![var(X)=E\left [ X^2 \right ]-\left ( E\left [ X \right ] \right )^2\\=\frac{31}{12}-\left ( \frac{17}{12} \right )^2\\=\frac{31}{12}-\frac{289}{144}\\=\frac{372-289}{144}\\=\frac{83}{144}\\=0.58](https://tex.z-dn.net/?f=var%28X%29%3DE%5Cleft%20%5B%20X%5E2%20%5Cright%20%5D-%5Cleft%20%28%20E%5Cleft%20%5B%20X%20%5Cright%20%5D%20%5Cright%20%29%5E2%5C%5C%3D%5Cfrac%7B31%7D%7B12%7D-%5Cleft%20%28%20%5Cfrac%7B17%7D%7B12%7D%20%5Cright%20%29%5E2%5C%5C%3D%5Cfrac%7B31%7D%7B12%7D-%5Cfrac%7B289%7D%7B144%7D%5C%5C%3D%5Cfrac%7B372-289%7D%7B144%7D%5C%5C%3D%5Cfrac%7B83%7D%7B144%7D%5C%5C%3D0.58)
40 percent of 250 = .4*250 = 100
100 seventh graders got the flu.
Answer:
765
Step-by-step explanation:
Answer:
a = 4.949
b = 4.949
c = 7
Step-by-step explanation:
c ( hypothenuse ) = 7
to find a, use sine
Sine = ![\frac{opposite}{hypothenuse\\}](https://tex.z-dn.net/?f=%5Cfrac%7Bopposite%7D%7Bhypothenuse%5C%5C%7D)
Sine 45 = ![\frac{a}{7}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7B7%7D)
sine of 45 is 0.707
0.707 = ![\frac{a}{7}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7B7%7D)
multiplt 7 on both sides:
0.707 x 7 =
x 7
a = 4.949
to find b, use cosine
Cosine = ![\frac{adjacent}{hypothenuse}](https://tex.z-dn.net/?f=%5Cfrac%7Badjacent%7D%7Bhypothenuse%7D)
Cos 45 = ![\frac{b}{7}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%7D%7B7%7D)
cos of 45 is 0.707
0.707 = ![\frac{b}{7}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%7D%7B7%7D)
multiply 7 on both sides:
0.707 x 7 =
x 7
b = 4.949
Answer:
omg
Step-by-step explanation:
omg omg omg omg omg what is this