4. Consider a gaussian probability density on the x axis p(x) = A exp [ - λ(x-a)²] λ >0, a, and A are constants (a) Sketch the graph of p(x) (b) Find the normalization constant A (c) Find the expectation values < x >, < x² > and the variance o
4. Consider a gaussian probability density on the x axis p(x) = A exp [ - λ(x-a)²] λ >0, a, and A are constants (a) Sketch the graph of p(x) (b) Find the normalization constant A (c) Find the expectation values < x >, < x² > and the variance o
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![4. Consider a gaussian probability density on the x axis
p(x) = A exp[- λ(x-a)² ]
λ>0, a, and A are constants
(a) Sketch the graph of p(x)
(b) Find the normalization constant A
(c) Find the expectation values < x >, < x² > and the variance o](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F62a79166-ba2c-43d7-9fa1-94c5c5be2063%2F2d5f5d04-1247-4d03-abf9-4ac1b7c99ca6%2F936np3u_processed.png&w=3840&q=75)
Transcribed Image Text:4. Consider a gaussian probability density on the x axis
p(x) = A exp[- λ(x-a)² ]
λ>0, a, and A are constants
(a) Sketch the graph of p(x)
(b) Find the normalization constant A
(c) Find the expectation values < x >, < x² > and the variance o
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VIEWStep 2: (a) Sketch the graph of the probability density function:
VIEWStep 3: (b) Calculate the normalization constant of the function:
VIEWStep 4: (c) Calculate the expectation value of the position:
VIEWStep 5: (c) Calculate the expectation value of the square of x:
VIEWStep 6: (c) Calculate the variance of the position:
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