When a certain basketball player takes his first shot in a game he succeeds with prob. 1/3. If he misses his first shot, he loses confidence and his second shot will go with prob. 1/4. If he misses his first 2 shots, his third shot will go with pro. 1/5. If he misses his first 3 shots, his fourth shot will go with prob. 1/6. If he misses his first 4 shots, the coach will remove hom from the game. Assume that the player keeps shooting until he succeeds or he is removed from the game. Let X denote the number of shots he misses until his first success or until he is removed from the game. Required:
a. Compute the p. m.f. of X
b. Compute E[X]

X : 0 1 2 3 4

P(x) : _ 0.333_0.167 _0.100_0.067__0.333

E(X) = 1.9

Step-by-step explanation:

From the question above:

X ; number of misses

For :

X = 0 ; P(X = 0) = 1/3 = 0.333

X = 1 ; misses first ; succeeds on second

P(X = 1) = 2/3 * 1/4 = 2/12 = 1/6 = 0.167

X = 2 ; misses first, misses second, succeeds on third

P(X = 2) = 2/3 * (1 - 1/4) * 1/5 = 2/3*3/4*1/5 = 6/60 = 1/10 = 0.10

X = 3 :misses first, misses second, misses third succeeds on fourth

P(X = 3) = 2/3 * 3/4 * (1 - 1/5) * 1/6 = 2/3*3/4*4/5*1/6 = 24/360 = 0.067

X= 4

P(X =4) = 2/3 * 3/4 * 4/5 * 5/6 = 120/ 360 = 1/3 = 0.333

X : 0 1 2 3 4

P(x) : _ 0.333_0.167 _0.100_0.067__0.333

E(X) :

Σx*p(x) = (0*0.333) + (1*0.167) + (2*0.100) + (3*0.067) + (4*0.333)

0 + 0.167 + 0.2 + 0.201 + 1.332

= 1.9

step-by-step explanation:

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!