Developing an e-learning analytics platform using AWS Lambda to process student data from Amazon RDS and visualized in Power BI

Based on your description, here is a basic Pulumi Python program. Shortly, here are the high-level actions it represents:

1. Creates an RDS MySQL instance to store student data.
2. Creates an AWS IAM role for lambda execution.
3. Creates a Lambda function to process student data.
4. Uses Amazon Secrets Manager to store a Power BI API Key.

This Python program sets the foundation for an e-learning analytics platform. However, some parts of the application would need separate handling, like designing the AWS Lambda function's logic to process and transform the student data into a format expected by Power BI and visualizing the data in Power BI (which is beyond Pulumi's scope).

Here's the Python code:

import pulumi
from pulumi_aws import rds, iam, lambda_, secretsmanager

# create a new RDS instance running MySQL
db_instance = rds.Instance('db-instance', 
    engine='mysql',
    instance_class='db.t2.micro',
    allocated_storage=20,
    name='sample',
    username='admin',
    password='password',
    skip_final_snapshot=True)

# create a new IAM Role for lambda 
role = iam.Role('LambdaExecutionRole',
    assume_role_policy='''{
    "Version": "2012-10-17",
    "Statement": [
        {
        "Action": "sts:AssumeRole",
        "Principal": {
            "Service": "lambda.amazonaws.com"
        },
        "Effect": "Allow",
        "Sid": ""
        }
    ]
    }''')

# create a Lambda function to process the data
func = lambda_.Function('lambdaFunction',
    role=role.arn,
    runtime='python3.6',
    handler='index.handler',
    s3_bucket='testBucket',
    s3_key='testKey')

# Save Power BI API Key in Secrets Manager
secret = secretsmanager.Secret('secretManager',
    name='powerBI-API-key',
    description='The API key for Power BI')

# Output the RDS instance endpoint and Power BI API Key ARN
pulumi.export('instanceEndpoint', db_instance.endpoint)
pulumi.export('powerBI_ApiKey_ARN', secret.arn)

Remember that you need to replace testBucket and testKey with the actual S3 bucket name and key where your Lambda function code is stored.

Relevant Pulumi registry resources:

• pulumi_aws.rds.Instance
• pulumi_aws.iam.Role
• pulumi_aws.lambda_.Function
• pulumi_aws.secretsmanager.Secret

Remember to replace the placeholders in the program with actual values. You'll also need to write the corresponding Lambda function code that connects to your RDS instance, fetches the data, processes the data, and interacts with the PowerBI API, this would go into the uploaded .zip in your S3 bucket.