Question

x= 0, 1, 2, 3, 4, 5

p(x)= 0.1,0.3,0.4,0.1,?,0.5

find p(4)

construct probability histogram to describe p(x)

Answer 1

Let $p(4)=y\ge0.$

Check

$$\sum_ip(x_i)=1$$

$$0.1+0.3+0.4+0.1+y+0.5=1$$

$$y=-0.4<0$$

We have a contradiction. Therefore such probability distribution is not possible. The task has no solution.