θ=0.5 θ=1 θ=2 θ=3
λ = 2
θ = 0.5
μ = 0.5
σ = 0.5
θ=0.5
0 2
1 0.270670566
2 0.036631278
3 0.004957504
4 0.000670925
5 9.07999E-05
draw the graph for
θ=1 θ=2 θ=3
The first θ=0.5 graph was drawn for you so follow the same procedure for the others.
To draw the graphs for θ=1, θ=2, and θ=3, you can follow the same procedure used to draw the graph for θ=0.5.
1. Identify the values for λ, θ, μ, and σ given in the problem statement. In this case, λ=2, θ=1, μ=0.5, and σ=0.5.
2. Use the formula for the normal distribution to calculate the corresponding y-values for each x-value:
P(x) = (1 / (σ * √(2π))) * e^(-0.5 * ((x - μ) / σ)^2)
Substitute the values of θ, μ, and σ into the formula:
P(x) = (1 / (0.5 * √(2π))) * e^(-0.5 * ((x - 0.5) / 0.5)^2)
3. Choose a range of x-values that covers the desired range for the graph. For example, you could choose x-values from -10 to 10 with a step of 0.1.
4. Plug each x-value into the formula from step 2 to calculate the corresponding y-values.
5. Plot the (x, y) pairs on a graph, with x-values on the x-axis and y-values on the y-axis.
Repeat steps 2-5 for each value of θ (1, 2, and 3) to get the graphs for each case.
Note: It's important to remember that the area under the curve represents the probability of the given θ value occurring.